[cig-commits] r6684 - geodyn/3D/MoSST/trunk/doc
sue at geodynamics.org
sue at geodynamics.org
Wed Apr 25 12:38:24 PDT 2007
Author: sue
Date: 2007-04-25 12:38:23 -0700 (Wed, 25 Apr 2007)
New Revision: 6684
Added:
geodyn/3D/MoSST/trunk/doc/mosst.lyx
Log:
mosst template lyx manual added, and in process of inserting governing equations
Added: geodyn/3D/MoSST/trunk/doc/mosst.lyx
===================================================================
--- geodyn/3D/MoSST/trunk/doc/mosst.lyx 2007-04-25 19:30:44 UTC (rev 6683)
+++ geodyn/3D/MoSST/trunk/doc/mosst.lyx 2007-04-25 19:38:23 UTC (rev 6684)
@@ -0,0 +1,12110 @@
+#LyX 1.4.3-4 created this file. For more info see http://www.lyx.org/
+\lyxformat 245
+\begin_document
+\begin_header
+\textclass book
+\begin_preamble
+\usepackage{hyperref}
+
+\let\myUrl\url
+\renewcommand{\url}[1]{(\myUrl{#1})}
+\end_preamble
+\language english
+\inputencoding auto
+\fontscheme default
+\graphics default
+\paperfontsize default
+\spacing single
+\papersize default
+\use_geometry true
+\use_amsmath 1
+\cite_engine basic
+\use_bibtopic false
+\paperorientation portrait
+\leftmargin 1in
+\topmargin 1in
+\rightmargin 1in
+\bottommargin 1in
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
+\defskip medskip
+\quotes_language swedish
+\papercolumns 1
+\papersides 2
+\paperpagestyle headings
+\tracking_changes false
+\output_changes true
+\end_header
+
+\begin_body
+
+\begin_layout Standard
+\noindent
+\align center
+
+\color none
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+thispagestyle{empty}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Title
+MoSST
+\end_layout
+
+\begin_layout Author
+© California Institute of Technology
+\newline
+Peter Olson, Wei Mi
+\newline
+Version 1.0
+\end_layout
+
+\begin_layout Date
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+today
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset LatexCommand \tableofcontents{}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset FloatList figure
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+raggedbottom
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\newpage
+
+\end_layout
+
+\begin_layout Chapter
+Preface
+\end_layout
+
+\begin_layout Section
+Who Will Use MoSST?
+\end_layout
+
+\begin_layout Standard
+The main audience for CIGMA is research scientists interested in ???????.
+ Examples of problems that can be solved are the development of tectonic
+ structure associated with extension and compression, especially where localizat
+ion is important.
+ You do not have to be an expert in finite element analysis or scientific
+ computing to use this software.
+\end_layout
+
+\begin_layout Section
+Citation
+\end_layout
+
+\begin_layout Standard
+Computational Infrastructure for Geodynamics (CIG) is making this source
+ code available to you in the hope that the software will enhance your research
+ in geophysics.
+ The underlying C code for the finite element package was donated to CIG
+ in July of 2005.
+ A number of individuals have contributed a significant portion of their
+ careers toward the development of Gale.
+ It is essential that you recognize these individuals in the normal scientific
+ practice by making appropriate acknowledgements.
+
+\end_layout
+
+\begin_layout Standard
+The code is based on the method described in
+\end_layout
+
+\begin_layout Itemize
+Moresi, L.N., F.
+ Dufour, and H.-B.
+ Mühlhaus (2003), A Lagrangian integration point finite element method for
+ large deformation modeling of viscoelastic geomaterials,
+\emph on
+J.
+ Comp.
+ Phys., 184
+\series bold
+,
+\series default
+\emph default
+ 476-497.
+
+\end_layout
+
+\begin_layout Standard
+The code was originally developed by the Victorian Partnership for Advanced
+ Computing (VPAC) and Louis Moresi's group at Monash University.
+ Walter Landry of CIG and Luke Hodkinson of VPAC have enhanced the code
+ to satisfy the requirements of the long-term tectonics community.
+ Roger Buck, Gus Correa, and Robert Bialas from the Lamont-Doherty Earth
+ Observatory, Columbia University, provided valuable user testing.
+ The Gale team requests that in your oral presentations and in your papers
+ that you indicate your use of this code and acknowledge the authors of
+ the code,
+\begin_inset LatexCommand \htmlurl[CIG]{www.geodynamics.org}
+
+\end_inset
+
+,
+\begin_inset LatexCommand \htmlurl[Victoria Partnership for Advanced Computing]{www.vpac.org}
+
+\end_inset
+
+, and
+\begin_inset LatexCommand \htmlurl[Monash University]{www.monash.edu}
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Section
+Support
+\end_layout
+
+\begin_layout Standard
+Gale development is supported by a grant from the National Science Foundation
+ to CIG, managed by the California Institute of Technology.
+ However, most of the software components below Gale have been developed
+ by the Victoria Partnership for Advanced Computing (VPAC) and Monash University.
+\end_layout
+
+\begin_layout Chapter
+Introduction
+\end_layout
+
+\begin_layout Section
+About MoSST
+\end_layout
+
+\begin_layout Standard
+Gale is a parallel, two- or three-dimensional, implicit finite element code
+ that solves problems related to orogenesis, rifting, and subduction with
+ coupling to surface erosion models.
+ Gale uses a hybrid particle-in-cell scheme which combines a deformable
+ mesh of computational points and a dense arrangement of mobile material
+ points.
+ The boundaries of the deformable mesh conform to the boundaries of the
+ material as the simulation progresses, but the interior is constrained
+ to remain as regular as possible.
+ The particles track history-dependent properties such as strain for strain-soft
+ening materials.
+ This allows Gale to simulate problems with large deformations and irregular
+ boundaries.
+\end_layout
+
+\begin_layout Standard
+CIG has developed Gale in response to community demand by building on existing
+ work by VPAC and Louis Moresi's group at Monash University.
+ The code is being released under the GNU General Public License.
+\end_layout
+
+\begin_layout Section
+MoSST Computational Approach and Governing Equations
+\end_layout
+
+\begin_layout Subsection
+Infrastructure
+\end_layout
+
+\begin_layout Standard
+Gale uses both a regular grid and particles.
+ The regular grid is used to solve differential equations, and particles
+ are used to track material properties (e.g., strain history).
+ Note that the regular grid can become distorted, since it may conform to
+ an uneven upper surface.
+\end_layout
+
+\begin_layout Subsection
+Units
+\end_layout
+
+\begin_layout Standard
+Gale has no internal knowledge of units.
+ So if you tell Gale that a box is 10 units across, it does not know or
+ care whether it is 10 cm or 10 km.
+ You only have to make sure that you are consistent.
+ For example, if you give velocities in cm/year, make sure that your viscosities
+ and lengths also use cm and years.
+
+\end_layout
+
+\begin_layout Subsection
+Basic Equations
+\end_layout
+
+\begin_layout Standard
+Christensen's non-dimensionalization
+\end_layout
+
+\begin_layout Paragraph*
+Symbols
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \[
+D=r_{o}-r_{i}=1,\,\frac{r_{i}}{r_{o}}=0.35,\, r_{i}=\frac{7}{13},\, r_{o}=\frac{20}{13}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $\nu:$
+\end_inset
+
+ kinematic viscosity
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $\eta:$
+\end_inset
+
+ magnetic diffusivity
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $\kappa:$
+\end_inset
+
+ thermal diffusivity
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $\mu:$
+\end_inset
+
+ magnetic permeability
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $\Omega:$
+\end_inset
+
+ basic rotating rate
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $ $
+\end_inset
+
+
+\begin_inset Formula $\rho:$
+\end_inset
+
+ density
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $\alpha:$
+\end_inset
+
+ thermal expansion coefficient
+\end_layout
+
+\begin_layout Paragraph*
+Scales
+\end_layout
+
+\begin_layout Standard
+length:
+\begin_inset Formula $D$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+time:
+\begin_inset Formula $\frac{D^{2}}{v}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+velocity:
+\begin_inset Formula $\frac{v}{D}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+temperature:
+\begin_inset Formula $\Delta T$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+magnetic field:
+\begin_inset Formula $(\rho\mu\eta\Omega)^{\frac{1}{2}}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+pressure:
+\begin_inset Formula $\rho\nu\Omega$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Paragraph*
+Parameters:
+\end_layout
+
+\begin_layout Standard
+Modified Rayleigh number:
+\begin_inset Formula $R_{a}=\frac{\alpha g_{o}\Delta TD}{\nu\Omega}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Ekman number:
+\begin_inset Formula $E_{c}=\frac{\nu}{\Omega D^{2}}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Prandtl number:
+\begin_inset Formula $P_{r}=\frac{\nu}{\kappa}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Magnetic Prandtl number:
+\begin_inset Formula $P_{m}=\frac{\nu}{\eta}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Dimensionless equations:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \[
+E_{c}\left(\frac{\partial\mathrm{\mathbf{u}}}{\partial t}+\mathrm{\mathbf{u}}\bullet\bigtriangledown\mathrm{\mathbf{u}}-\bigtriangledown^{2}\mathrm{\mathbf{u}}\right)+2\hat{\mathrm{\mathbf{z}\times u=-\bigtriangledown\mathit{P+R_{a}\frac{\mathrm{\mathbf{r}}}{r_{o}}\mathit{\Upsilon+\frac{1}{P_{m}}\left(\bigtriangledown\times\mathrm{\mathbf{B}}\right)\times\mathrm{\mathbf{B}}}}}}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \[
+\frac{\partial\mathrm{\mathbf{B}}}{\partial t}\]
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+The head bar denotes the unit vector.
+\end_layout
+
+\begin_layout Standard
+Kuang?s non-dimensionalization
+\end_layout
+
+\begin_layout Standard
+Symbols:
+\end_layout
+
+\begin_layout Standard
+radial of the outer core
+\end_layout
+
+\begin_layout Standard
+kinematic viscosity
+\end_layout
+
+\begin_layout Standard
+magnetic diffusivity
+\end_layout
+
+\begin_layout Standard
+thermal diffusivity
+\end_layout
+
+\begin_layout Standard
+magnetic permeability
+\end_layout
+
+\begin_layout Standard
+basic rotating rate
+\end_layout
+
+\begin_layout Standard
+density
+\end_layout
+
+\begin_layout Standard
+thermal expansion coefficient
+\end_layout
+
+\begin_layout Standard
+Scales:
+\end_layout
+
+\begin_layout Standard
+length:
+\end_layout
+
+\begin_layout Standard
+time:
+\end_layout
+
+\begin_layout Standard
+velocity:
+\end_layout
+
+\begin_layout Standard
+temperature:
+\end_layout
+
+\begin_layout Standard
+magnetic field:
+\end_layout
+
+\begin_layout Standard
+pressure:
+\end_layout
+
+\begin_layout Standard
+Parameters
+\end_layout
+
+\begin_layout Standard
+Rossby number:
+\end_layout
+
+\begin_layout Standard
+Prandtl number:
+\end_layout
+
+\begin_layout Standard
+Rayleigh number:
+\end_layout
+
+\begin_layout Standard
+Ekman number:
+\end_layout
+
+\begin_layout Standard
+Dimensionless equations:
+\end_layout
+
+\begin_layout Standard
+Note that r in the buoyant force has been normalized with ro, while it is
+ normalized with D in Christensen?s equation.
+\end_layout
+
+\begin_layout Standard
+Parameter conversion:
+\end_layout
+
+\begin_layout Standard
+1.
+ Conducting state
+\end_layout
+
+\begin_layout Standard
+In Christensen,
+\end_layout
+
+\begin_layout Standard
+, (2.1)
+\end_layout
+
+\begin_layout Standard
+In Kuang,
+\end_layout
+
+\begin_layout Standard
+.
+ (2.2)
+\end_layout
+
+\begin_layout Standard
+For benchmarking, (2.1) and (2.2) must be identical.
+ Therefore
+\end_layout
+
+\begin_layout Standard
+(2.3)
+\end_layout
+
+\begin_layout Standard
+where .
+\end_layout
+
+\begin_layout Standard
+2.
+ Non-dimensional parameters
+\end_layout
+
+\begin_layout Standard
+(2.4)
+\end_layout
+
+\begin_layout Standard
+(2.5)
+\end_layout
+
+\begin_layout Standard
+(2.6)
+\end_layout
+
+\begin_layout Standard
+(2.7)
+\end_layout
+
+\begin_layout Standard
+3.
+ Non-dimensional physical fields
+\end_layout
+
+\begin_layout Standard
+(2.8)
+\end_layout
+
+\begin_layout Standard
+(2.9)
+\end_layout
+
+\begin_layout Standard
+4.
+ Other physical quantities
+\end_layout
+
+\begin_layout Standard
+(2.10)
+\end_layout
+
+\begin_layout Standard
+(2.11)
+\end_layout
+
+\begin_layout Standard
+Initial conditions
+\end_layout
+
+\begin_layout Standard
+The initial conditions on radial magnetic field in Christensen can be written
+ as,
+\end_layout
+
+\begin_layout Standard
+Thus, in Kuang?s model, the coefficient should be,
+\end_layout
+
+\begin_layout Standard
+The initial conditions on azimuzal magnetic field is,
+\end_layout
+
+\begin_layout Standard
+In kuang?s model, the initial conditions can be rescaled as,
+\end_layout
+
+\begin_layout Standard
+The initial perturbation of the temperature is
+\end_layout
+
+\begin_layout Standard
+where , x being 2r-ro-ri
+\end_layout
+
+\begin_layout Standard
+In Kuang?s model,
+\end_layout
+
+\begin_layout Standard
+where , x being
+\end_layout
+
+\begin_layout Standard
+Benchmark cases
+\end_layout
+
+\begin_layout Standard
+Case 2 : Conducting and freely rotating inner core
+\end_layout
+
+\begin_layout Standard
+Christensen?s parameters:
+\end_layout
+
+\begin_layout Standard
+,
+\end_layout
+
+\begin_layout Standard
+,
+\end_layout
+
+\begin_layout Standard
+Kuang?s parameters:
+\end_layout
+
+\begin_layout Standard
+MoSST set up
+\end_layout
+
+\begin_layout Standard
+KICBV = 1 (no slip at ICB)
+\end_layout
+
+\begin_layout Standard
+KICMV = 1 (no slip at CMB)
+\end_layout
+
+\begin_layout Standard
+KICBT = 1 (fixed heat flux at ICB)
+\end_layout
+
+\begin_layout Standard
+KCMBT = 1 (fixed heat flux at CMB)
+\end_layout
+
+\begin_layout Standard
+k_icrot = 1 (only axial differential rotation )
+\end_layout
+
+\begin_layout Standard
+navfb = 70 ( truncation level for artificial diffision of B)
+\end_layout
+
+\begin_layout Standard
+navft = 70 ( truncation level for artificial diffision of T)
+\end_layout
+
+\begin_layout Standard
+navfv1 = 70 ( truncation level for artificial diffision of v1) (miner =
+ 16)
+\end_layout
+
+\begin_layout Standard
+navfv1 = 70 ( truncation level for artificial diffision of v2)
+\end_layout
+
+\begin_layout Standard
+Estimation
+\end_layout
+
+\begin_layout Standard
+Time scale
+\end_layout
+
+\begin_layout Standard
+=0.0845tc
+\end_layout
+
+\begin_layout Standard
+tc~15, tk~1
+\end_layout
+
+\begin_layout Standard
+temperature scale
+\end_layout
+
+\begin_layout Standard
+magnetic field
+\end_layout
+
+\begin_layout Standard
+--? E_b ~ 1.45
+\end_layout
+
+\begin_layout Standard
+? E_v ~ 50.03
+\end_layout
+
+\begin_layout Subsection
+Gravity
+\end_layout
+
+\begin_layout Section
+MoSST History
+\end_layout
+
+\begin_layout Standard
+Gale arose from discussions at an NSF-sponsored workshop on Tectonic Modeling
+ held in Breckenridge, Colorado, in June 2005; see
+\begin_inset LatexCommand \htmlurl[Geodynamic Modeling of Tectonics Processes 2005 workshop report]{www.geodynamics.org/cig/workinggroups/long/workshops/2005/issues}
+
+\end_inset
+
+.
+ At that workshop, members of the tectonics community advocated that CIG
+ develop a new open-source software package based on the Arbitrary Lagrangian
+ Eulerian (ALE) method for solving tectonic problems.
+ The ALE method, as it is implemented in the tectonics community, was developed
+ primarily at Dalhousie University in Canada.
+ It solves a Stokes flow problem on an Eulerian grid and uses a Lagrangian
+ grid to track material properties and to integrate strain.
+ This method has seen a great deal of use in crustal and lithospheric deformatio
+n problems such as orogenesis, rifting, and subduction, as well as in coupling
+ to surface erosion models, and has been employed for deeper mantle dynamics
+ problems.
+ Gale is an open-source code that we hope will be at least as useful as
+ SOPALE and MicroFEM
+\begin_inset LatexCommand \cite{Fullsack}
+
+\end_inset
+
+ for addressing these research areas
+\color none
+, with the addition of 3D capability.
+ In the future, Gale will run benchmarks such as extension and shortening,
+ as well as the traditional subduction model as shown in Fig.
+
+\begin_inset LatexCommand \ref{fig:General-subduction-model}
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+The development of Gale was jump-started by building on top of Underworld
+
+\begin_inset LatexCommand \cite{Underworld}
+
+\end_inset
+
+, a mantle convection code developed by Louis Moresi's group at Monash and
+ the Victorian Partnership for Advanced Computing (VPAC).
+ Underworld was created as a parallel version of Ellipsis3D
+\begin_inset LatexCommand \cite{Ellipsis}
+
+\end_inset
+
+, a mantle convection code which grew out of CitCom
+\begin_inset LatexCommand \cite{Citcom}
+
+\end_inset
+
+.
+ Walter Landry of CIG and Luke Hodkinson of VPAC are the primary developers
+ of the Gale-specific components.
+ Roger Buck, Robert Bialis, and Gus Correa of Lamont-Doherty Earth Observatory,
+ Columbia University, provided valuable user testing.
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float figure
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Caption
+\begin_inset LatexCommand \label{fig:General-subduction-model}
+
+\end_inset
+
+General subduction model from
+\begin_inset LatexCommand \cite{Fullsack}
+
+\end_inset
+
+.
+ The basic subduction model can be modified by introducing isostasy and/or
+ boundary mass fluxes.
+ (a) Flexural or local isostasy.
+ Every Eulerian column is displaced by the corresponding local or flexural
+ deflection
+\emph on
+w
+\emph default
+ of the base.
+ (b) Mass fluxes crossing the boundaries may be: (1) the tectonic flux
+\emph on
+t
+\emph default
+
+\begin_inset Formula $^{\text{+}}$
+\end_inset
+
+ into the domain, due to tectonic convergence; (2) the deposition flux
+\begin_inset Formula $\text{e}^{+}$
+\end_inset
+
+ onto the domain, due to surface processes; (3) the deposition flux
+\begin_inset Formula $\text{e}^{-}$
+\end_inset
+
+ from the domain, due to surface processes; (4) the crustal subduction flux
+
+\begin_inset Formula $\text{cs}^{-}$
+\end_inset
+
+ from the domain, due to the entrainment of crustal material from the subducting
+ plate.
+
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Graphics
+ filename ../../Gale/documentation/images/GALE_image1.eps
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Chapter
+Installation and Getting Help
+\end_layout
+
+\begin_layout Section
+Introduction
+\end_layout
+
+\begin_layout Standard
+Installation of Gale on a desktop or laptop machine is, in most cases, very
+ easy.
+ Binary packages have been created for the most common platforms, i.e., Linux,
+ Mac OS X, and Windows.
+ Installation on other architectures or on parallel machines requires building
+ the software from the source code, which can be difficult for inexperienced
+ users.
+
+\end_layout
+
+\begin_layout Section
+Binaries
+\end_layout
+
+\begin_layout Standard
+If you do not need to run on parallel machines, the easiest way to install
+ Gale is to download binaries for your platform from the
+\begin_inset LatexCommand \htmlurl[Gale website]{geodynamics.org/cig/software/packages/long/gale/}
+
+\end_inset
+
+.
+ Then you can run Gale from the command line or DOS prompt.
+ CIG provides binaries for Linux, Mac OS X (10.4 or greater), and Windows
+ (2000 and XP).
+\end_layout
+
+\begin_layout Section
+Building from Source
+\end_layout
+
+\begin_layout Standard
+Read this only if the binaries are not sufficient for you.
+
+\end_layout
+
+\begin_layout Subsection
+System Requirements
+\end_layout
+
+\begin_layout Standard
+Gale works on a variety of computational platforms and has been tested on
+ workstations running
+\end_layout
+
+\begin_layout Itemize
+Mac OS X 10.4.6 (G4 and G5)
+\end_layout
+
+\begin_layout Itemize
+Windows 2000 and XP SP2
+\end_layout
+
+\begin_layout Itemize
+RedHat Fedora Core 5 (x86)
+\end_layout
+
+\begin_layout Itemize
+OpenSuse 10.0 (x86)
+\end_layout
+
+\begin_layout Itemize
+Gentoo (x86)
+\end_layout
+
+\begin_layout Itemize
+Debian stable (x86 and AMD64), testing (x86), and unstable (x86)
+\end_layout
+
+\begin_layout Standard
+Gale has also been tested on clusters running Redhat 7.2 (x86) and RedHat
+ Enterprise Linux 3 (EM64T).
+\end_layout
+
+\begin_layout Subsection
+Dependencies
+\end_layout
+
+\begin_layout Standard
+In order to build Gale, you must have the headers and development libraries
+ for
+\end_layout
+
+\begin_layout Itemize
+MPI
+\end_layout
+
+\begin_layout Itemize
+PETSc 2.3.2
+\end_layout
+
+\begin_layout Itemize
+libxml2
+\end_layout
+
+\begin_layout Standard
+You must also have python 2.2.1 or greater installed.
+ If you do not already have MPI, then in many cases PETSc can install a
+ version for you.
+ Installing PETSc also requires a Blas/Lapack implementation.
+\end_layout
+
+\begin_layout Subsection
+\begin_inset LatexCommand \label{sec:Downloading-the-Code}
+
+\end_inset
+
+Downloading the Code
+\end_layout
+
+\begin_layout Standard
+You can get the source for the latest release from the
+\begin_inset LatexCommand \htmlurl[Gale website]{geodynamics.org/cig/software/packages/long/gale/}
+
+\end_inset
+
+.
+ In that tarball is the file INSTALL.
+ For some platforms, there are platform-specific instructions.
+ Generally, the hardest part is not installing Gale itself, but PETSc.
+\end_layout
+
+\begin_layout Subsubsection
+Source Code Repository (Experts Only)
+\end_layout
+
+\begin_layout Standard
+Advanced users and software developers may be interested in downloading
+ the latest Gale source code directly from the CIG source code repository,
+ instead of using the prepared source package.
+ To check whether you have a subversion client installed on your machine,
+ type:
+\end_layout
+
+\begin_layout LyX-Code
+svn
+\end_layout
+
+\begin_layout Standard
+You should get a response that looks something like this:
+\end_layout
+
+\begin_layout LyX-Code
+Type `svn help' for usage.
+\end_layout
+
+\begin_layout Standard
+Otherwise, you will need to download and install a Subversion client, available
+ at the
+\begin_inset LatexCommand \htmlurl[Subversion Website]{subversion.tigris.org/project_packages.html}
+
+\end_inset
+
+.
+ Then the code can be checked out with the following command:
+\end_layout
+
+\begin_layout LyX-Code
+svn checkout http://geodynamics.org/svn/cig/long/3D/Gale/trunk Gale
+\end_layout
+
+\begin_layout LyX-Code
+
+\end_layout
+
+\begin_layout Section
+Support
+\end_layout
+
+\begin_layout Standard
+The primary point of support for Gale is the
+\begin_inset LatexCommand \url[CIG Long-Term Crustal Dynamics Mailing List]{cig-long at geodynamics.org}
+
+\end_inset
+
+.
+ Feel free to send questions, comments, feature requests, and bugs to the
+ list.
+ The mailing list is archived at
+\end_layout
+
+\begin_layout LyX-Code
+\begin_inset LatexCommand \htmlurl[cig-long Archives]{geodynamics.org/pipermail/cig-long/}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+You may also use the bug tracker
+\end_layout
+
+\begin_layout LyX-Code
+\begin_inset LatexCommand \htmlurl[Roundup]{geodynamics.org/roundup}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+to submit bugs and requests for new features.
+\end_layout
+
+\begin_layout Chapter
+Running Gale
+\end_layout
+
+\begin_layout Section
+Gale Usage
+\end_layout
+
+\begin_layout Standard
+If you downloaded binaries for your platform, you can run the Gale executable
+ directly.
+ For example,
+\end_layout
+
+\begin_layout LyX-Code
+./Gale-1_2_0 input/extension.xml
+\end_layout
+
+\begin_layout Standard
+will output
+\end_layout
+
+\begin_layout LyX-Code
+TimeStep = 1, Start time = 0 + 0 prev timeStep dt
+\end_layout
+
+\begin_layout LyX-Code
+TimeStep = 2, Start time = 0 + 0.0291667 prev timeStep dt
+\end_layout
+
+\begin_layout LyX-Code
+TimeStep = 3, Start time = 0.0291667 + 0.0283326 prev timeStep dt
+\end_layout
+
+\begin_layout LyX-Code
+TimeStep = 4, Start time = 0.0574992 + 0.0274655 prev timeStep dt
+\end_layout
+
+\begin_layout LyX-Code
+TimeStep = 5, Start time = 0.0849647 + 0.0265162 prev timeStep dt
+\end_layout
+
+\begin_layout LyX-Code
+...
+\end_layout
+
+\begin_layout Standard
+If you do not specify an input file, you will get an error like
+\end_layout
+
+\begin_layout LyX-Code
+
+\size small
+Error in _AbstractContext_New: The dictionary is empty, meaning no input
+ parameters have been feed
+\end_layout
+
+\begin_layout LyX-Code
+
+\size small
+into your program.
+ Perhaps you've forgot to pass any input files ( or command-line arguments
+ ) in.
+\end_layout
+
+\begin_layout LyX-Code
+
+\size small
+Gale: build/StGermain/Base/IO/src/Journal.c:603: Journal_Firewall: Assertion
+ `expression' failed.
+\end_layout
+
+\begin_layout LyX-Code
+
+\size small
+p0_27845: p4_error: interrupt SIGx: 6
+\end_layout
+
+\begin_layout LyX-Code
+
+\end_layout
+
+\begin_layout Standard
+If Gale cannot find the file, you will get a different error:
+\end_layout
+
+\begin_layout LyX-Code
+
+\size small
+Error: File input/extension.xml doesn't exist, not readable, or not valid.
+\end_layout
+
+\begin_layout LyX-Code
+
+\size small
+Gale: build/StGermain/Base/IO/src/Journal.c:603: Journal_Firewall: Assertion
+ `expression' failed.
+\end_layout
+
+\begin_layout LyX-Code
+
+\size small
+p0_16810: p4_error: interrupt SIGx: 6
+\end_layout
+
+\begin_layout Standard
+Due to quirks in some implementations of MPI, you may have to specify the
+ complete path to the input file (e.g.,
+\family typewriter
+./Gale-1_2_0 /home/juser/gale/input/extension.xml
+\family default
+).
+\end_layout
+
+\begin_layout Standard
+In general, Gale does not have many defaults, so almost everything must
+ be specified in the input file.
+ For examples of how to create your own input files, see Chapter
+\begin_inset LatexCommand \ref{cha:Cookbooks}
+
+\end_inset
+
+.
+ For a complete description of the input file format, see Appendix
+\begin_inset LatexCommand \ref{cha:Input-File-Format}
+
+\end_inset
+
+.
+
+\end_layout
+
+\begin_layout Standard
+If you compile Gale yourself, you can run it from where you installed it.
+ If running in parallel on your own machine, prepend
+\family typewriter
+mpirun
+\family default
+ or
+\family typewriter
+mpiexec
+\family default
+ (depending on your local implementation of MPI).
+ For example, if your computer has two processors, then
+\end_layout
+
+\begin_layout LyX-Code
+mpirun -np 2 bin/Gale /home/juser/gale/input/extension.xml
+\end_layout
+
+\begin_layout Standard
+will use both processors.
+\end_layout
+
+\begin_layout Standard
+The
+\family typewriter
+extension.xml
+\family default
+ example should run for 100 time steps and generate a great deal of output
+ in the
+\family typewriter
+output.extension
+\family default
+ directory.
+ There are also examples of shortening, subduction, and relaxation of topography.
+\end_layout
+
+\begin_layout Standard
+Gale uses PETSc's GMRES linear solver by default.
+ However, PETSc has a facility where you can use command line arguments
+ to change the solver.
+ For example, on serial machines with small problems, a direct solve can
+ be much faster than GMRES.
+ To use a direct LU solve, you only need to append arguments to the command
+ line
+\end_layout
+
+\begin_layout LyX-Code
+./Gale-1_2_0 input/extension.xml -pc_type lu -ksp_type preonly
+\end_layout
+
+\begin_layout Standard
+You can also change the default values of
+\family typewriter
+extension.xml
+\family default
+ without modifying that file by appending arguments.
+ For example, to just change the number of time steps from the default value
+ 100 to 10, use the following command
+\end_layout
+
+\begin_layout LyX-Code
+./Gale-1_2_0 input/extension.xml --maxTimeSteps=10
+\end_layout
+
+\begin_layout Standard
+You can append any number of modified parameters in one unbroken line
+\end_layout
+
+\begin_layout LyX-Code
+
+\size small
+./Gale-1_2_0 input/extension.xml --maxTimeSteps=10 --dim=3 --elementResI=64
+
+\end_layout
+
+\begin_layout LyX-Code
+
+\size small
+--elementResJ=64 --elementResK=64 --particlesPerCell=60 --dumpEvery=10
+\end_layout
+
+\begin_layout Section
+Output and Visualization
+\end_layout
+
+\begin_layout Standard
+The sample input files will produce a directory in which you will find a
+ number of
+\family typewriter
+.dat
+\family default
+,
+\family typewriter
+.txt
+\family default
+, and
+\family typewriter
+\color none
+.vtk
+\family default
+ files.
+ The formats of the
+\family typewriter
+.dat
+\family default
+ and
+\family typewriter
+.txt
+\family default
+ files are described fully in Appendix
+\begin_inset LatexCommand \ref{cha:Output-File-Format}
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+The default setting is to create files for every time step.
+ To change the frequency of creating the
+\family typewriter
+.dat
+\family default
+ files, you need to change the parameter
+\family typewriter
+checkpointEvery
+\family default
+.
+ For example, if you modify the line with
+\family typewriter
+checkpointEvery
+\family default
+ to
+\end_layout
+
+\begin_layout LyX-Code
+<param name="checkpointEvery">25</param>
+\end_layout
+
+\begin_layout Standard
+then the
+\family typewriter
+.dat
+\family default
+ files will only be created every 25 time steps.
+ You can change the value to any number you want.
+ On the other hand, to change the frequency for creating
+\family typewriter
+.txt
+\family default
+ and
+\family typewriter
+.vtk
+\family default
+ files, you need to change the parameter
+\family typewriter
+dumpEvery
+\family default
+.
+\end_layout
+
+\begin_layout LyX-Code
+<param name="dumpEvery">25</param>
+\end_layout
+
+\begin_layout Quote
+
+\color red
+Note:
+\color none
+ In order to get viscosity information out, you must add a
+\family typewriter
+StoreViscosity
+\family default
+ struct to your rheology as in Section
+\begin_inset LatexCommand \ref{sec:Viscous-Material}
+
+\end_inset
+
+ (see also Section
+\begin_inset LatexCommand \ref{sub:StoreViscosity}
+
+\end_inset
+
+).
+ This is already done in all of the example input files.
+\end_layout
+
+\begin_layout Standard
+
+\color none
+There are a number of different options for visualizing the data.
+ The easiest way is to use the
+\family typewriter
+.vtk
+\family default
+ files.
+ These files are in a standard, self-describing file format that can be
+ easily visualized with several different visualization programs, e.g.,
+\begin_inset LatexCommand \htmlurl[ParaView]{paraview.org}
+
+\end_inset
+
+,
+\begin_inset LatexCommand \htmlurl[MayaVI]{mayavi.sf.net}
+
+\end_inset
+
+, and
+\begin_inset LatexCommand \htmlurl[Visit]{www.llnl.gov/visit}
+
+\end_inset
+
+.
+ ParaView is recommended as it is easy to get working, easy to use, and
+ scales to large data sets.
+\end_layout
+
+\begin_layout Standard
+Another option is to use the Matlab scripts in the
+\family typewriter
+tools/
+\family default
+ directory.
+ These scripts only work in 2D and only when running simulations with yielding
+ material.
+\end_layout
+
+\begin_layout Standard
+The last option is to use a spreadsheet program such as Excel.
+ This is very limited, as you only see the location of the particles.
+ You cannot visualize the viscosity or degree of yielding of the particles,
+ nor can you visualize the fields (e.g.
+ strain rate, pressure, etc.).
+\end_layout
+
+\begin_layout Subsection
+Visualization with ParaView
+\begin_inset LatexCommand \label{sub:Visualization-with-ParaView}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\color none
+To visualize step #10 of
+\family typewriter
+input/extension.xml
+\family default
+,
+\end_layout
+
+\begin_layout Enumerate
+
+\color none
+Start Paraview and open new data:
+\family sans
+File
+\family default
+
+\begin_inset Formula $\triangleright$
+\end_inset
+
+
+\family sans
+Open Data
+\end_layout
+
+\begin_deeper
+\begin_layout Standard
+\begin_inset Float figure
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Standard
+
+\color none
+\begin_inset Graphics
+ filename ../../Gale/documentation/images/Paraview_open_data.png
+ lyxscale 50
+ scale 50
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\newpage
+
+\end_layout
+
+\end_deeper
+\begin_layout Enumerate
+A file dialog screen will appear.
+ Navigate to the output directory and select
+\family typewriter
+\color none
+pressure.0.00010.vtk
+\family default
+.
+ Paraview will display a pseudocolor plot of the pressure.
+\end_layout
+
+\begin_deeper
+\begin_layout Standard
+\begin_inset Float figure
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Standard
+
+\color none
+\begin_inset Graphics
+ filename ../../Gale/documentation/images/Paraview_pressure.png
+ lyxscale 50
+ scale 50
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_deeper
+\begin_layout Enumerate
+You can also look at the velocities and strains by opening
+\family typewriter
+\color none
+fields.0.00010.vtk
+\family default
+ (with
+\family sans
+File
+\family default
+
+\begin_inset Formula $\triangleright$
+\end_inset
+
+
+\family sans
+Open Data
+\family default
+).
+ By default, Paraview will obscure the pressure with the velocity magnitude.
+\end_layout
+
+\begin_deeper
+\begin_layout Standard
+
+\color none
+\begin_inset Float figure
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Standard
+
+\color none
+\begin_inset Graphics
+ filename ../../Gale/documentation/images/Paraview_vmag.png
+ lyxscale 50
+ scale 50
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\newpage
+
+\end_layout
+
+\end_deeper
+\begin_layout Enumerate
+You can remove the velocity magnitude by clicking on the ``eye'' symbol
+ next to
+\family typewriter
+\color none
+fields.0.00010.vtk
+\family default
+, graying it out.
+\newline
+
+\newline
+
+\begin_inset Graphics
+ filename ../../Gale/documentation/images/Paraview_grey_eye.png
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Enumerate
+Now you can plot the velocity as arrows on top of the pressure: Click on
+ the ``Glyph'' symbol
+\newline
+
+\newline
+
+\begin_inset Graphics
+ filename ../../Gale/documentation/images/Paraview_glyph.png
+
+\end_inset
+
+
+\newline
+
+\newline
+and then press the green ``Accept'' button.
+ The result will look like this:
+\end_layout
+
+\begin_deeper
+\begin_layout Standard
+\begin_inset Float figure
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Standard
+\begin_inset Graphics
+ filename ../../Gale/documentation/images/Paraview_pressure_velocity.png
+ lyxscale 50
+ scale 50
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\newpage
+
+\end_layout
+
+\end_deeper
+\begin_layout Enumerate
+You can also visualize the Strain Rate Invariant: Click on the grayed-out
+ eye next to
+\family typewriter
+\color none
+fields.0.00010.vtk
+\family default
+, and then click on the ``Display'' tab.
+\end_layout
+
+\begin_deeper
+\begin_layout Standard
+\begin_inset Float figure
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Standard
+
+\color none
+\begin_inset Graphics
+ filename ../../Gale/documentation/images/Paraview_v_vector.png
+ lyxscale 50
+ scale 50
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_deeper
+\begin_layout Enumerate
+Finish by clicking on the drop down list to the right of ``Color by'' and
+ selecting ``Point StrainRateInvariantField.''
+\end_layout
+
+\begin_deeper
+\begin_layout Standard
+\begin_inset Float figure
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Standard
+\begin_inset Graphics
+ filename ../../Gale/documentation/images/Paraview_strainrate.png
+ lyxscale 50
+ scale 50
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\newpage
+
+\end_layout
+
+\end_deeper
+\begin_layout Enumerate
+Now look at the particles.
+ Starting over, open
+\family typewriter
+\color none
+particles.0.00010.vtk
+\family default
+ and click on the ``Glyph'' button.
+ Change Glyph to Sphere0, Scale Mode to ``Data Scaling Off,'' the Scale
+ Factor to 0.01, and press the Accept button.
+\end_layout
+
+\begin_deeper
+\begin_layout Standard
+
+\color none
+\begin_inset Float figure
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Standard
+
+\color none
+\begin_inset Graphics
+ filename ../../Gale/documentation/images/Paraview_particles_viscosity.png
+ lyxscale 50
+ scale 50
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\color none
+This displays the viscosity of the particles.
+ The blue points represent low viscosity material, either the material at
+ the bottom that was originally low viscosity, or the material that has
+ yielded.
+
+\newpage
+
+\end_layout
+
+\end_deeper
+\begin_layout Enumerate
+To see explicitly which material has yielded, click on the ``Display'' tab
+ and change the ``Color by'' box to ``Point Yielding_fraction.''
+\end_layout
+
+\begin_deeper
+\begin_layout Standard
+\begin_inset Float figure
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Standard
+\begin_inset Graphics
+ filename ../../Gale/documentation/images/Paraview_particles_yielding.png
+ lyxscale 50
+ scale 50
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_deeper
+\begin_layout Subsection
+Visualization with Matlab or Octave
+\end_layout
+
+\begin_layout Standard
+
+\color none
+Gale includes a number of Matlab visualization scripts in the
+\family typewriter
+tools/
+\family default
+ directory.
+ The scripts also work with Octave, a free Matlab clone.
+ However, they only work for 2D runs with yielding rheologies.
+ To use these scripts,
+\end_layout
+
+\begin_layout Enumerate
+
+\color none
+Navigate into the
+\family typewriter
+tools/
+\family default
+ directory
+\end_layout
+
+\begin_layout Enumerate
+
+\color none
+Modify
+\family typewriter
+fname
+\family default
+ in
+\family typewriter
+PlotGaleOutput.m
+\family default
+ to point to the output directory
+\end_layout
+
+\begin_layout Enumerate
+
+\color none
+Change
+\family typewriter
+step
+\family default
+ to the time step
+\end_layout
+
+\begin_layout Enumerate
+
+\color none
+Start Matlab or Octave and type
+\end_layout
+
+\begin_deeper
+\begin_layout LyX-Code
+PlotGaleOutput
+\end_layout
+
+\begin_layout Enumerate
+Using Octave to visualize the 10th step of
+\family typewriter
+input/extension.xml
+\family default
+ results in
+\end_layout
+
+\begin_deeper
+\begin_layout Standard
+\begin_inset Graphics
+ filename ../../Gale/documentation/images/Octave_fig1.png
+ lyxscale 75
+ scale 75
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Graphics
+ filename ../../Gale/documentation/images/Octave_fig2.png
+ lyxscale 75
+ scale 75
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Graphics
+ filename ../../Gale/documentation/images/Octave_fig3.png
+ lyxscale 75
+ scale 75
+
+\end_inset
+
+
+\newpage
+
+\end_layout
+
+\end_deeper
+\begin_layout Enumerate
+Using Matlab results in
+\end_layout
+
+\begin_deeper
+\begin_layout Standard
+\begin_inset Graphics
+ filename ../../Gale/documentation/images/Matlab_fig111.png
+ scale 75
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Graphics
+ filename ../../Gale/documentation/images/Matlab_fig112.png
+ scale 75
+
+\end_inset
+
+
+\end_layout
+
+\end_deeper
+\end_deeper
+\begin_layout Subsection
+Visualization with Excel
+\end_layout
+
+\begin_layout Standard
+
+\color none
+You can set the DumpSwarm plugin (see Section
+\begin_inset LatexCommand \ref{sec:.txt-Files-(Particle}
+
+\end_inset
+
+) to directly output
+\family typewriter
+.csv
+\family default
+ files, which you can use for limited visualization with a spreadsheet program
+ such as Excel.
+ For example, for the
+\family typewriter
+input/extension.xml
+\family default
+ input file,
+\end_layout
+
+\begin_layout Enumerate
+
+\color none
+Open the file
+\family typewriter
+output.extension/particles.00010.csv
+\family default
+ with your spreadsheet program.
+ Select the second two columns
+\end_layout
+
+\begin_deeper
+\begin_layout Standard
+
+\color none
+\begin_inset Float figure
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Standard
+
+\color none
+\begin_inset Graphics
+ filename ../../Gale/documentation/images/Gnumeric_two_columns.png
+ lyxscale 50
+ scale 50
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_deeper
+\begin_layout Enumerate
+Create a chart
+\end_layout
+
+\begin_deeper
+\begin_layout Standard
+\begin_inset Float figure
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Standard
+
+\color none
+\begin_inset Graphics
+ filename ../../Gale/documentation/images/Gnumeric_new_chart.png
+ lyxscale 50
+ scale 50
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\newpage
+
+\end_layout
+
+\end_deeper
+\begin_layout Enumerate
+Select an XY plot and press Insert
+\end_layout
+
+\begin_deeper
+\begin_layout Standard
+\begin_inset Float figure
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Standard
+\begin_inset Graphics
+ filename ../../Gale/documentation/images/Gnumeric_xy_plot.png
+ lyxscale 75
+ scale 75
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\newpage
+
+\end_layout
+
+\end_deeper
+\begin_layout Enumerate
+Then press anywhere on the spreadsheet, and you will have a plot of the
+ particles.
+\end_layout
+
+\begin_deeper
+\begin_layout Standard
+\begin_inset Float figure
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Standard
+\begin_inset Graphics
+ filename ../../Gale/documentation/images/Gnumeric_final.png
+ lyxscale 50
+ scale 50
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_deeper
+\begin_layout LyX-Code
+
+\end_layout
+
+\begin_layout Section
+Gauging Accuracy
+\end_layout
+
+\begin_layout Standard
+Gale makes a number of approximations.
+ Before trusting any results you get from Gale, you must vary a number of
+ parameters to insure that the results are not an artifact of Gale's approximati
+ons.
+ Specifically, for every simulation, vary the resolution (
+\family typewriter
+elementResI
+\family default
+,
+\family typewriter
+elementResJ
+\family default
+,
+\family typewriter
+elementResK
+\family default
+) and the number of particles in each element (
+\family typewriter
+particlesPerCell
+\family default
+).
+ For problems with inflow boundaries (see Sections
+\begin_inset LatexCommand \ref{sec:Viscous-In-Outflow}
+
+\end_inset
+
+ and
+\begin_inset LatexCommand \ref{sub:Flux-Boundary-Conditions}
+
+\end_inset
+
+), you must vary the size of the boundary box.
+ In addition, depending on the boundary conditions, you may need to vary
+ the size of the box (
+\family typewriter
+minX
+\family default
+,
+\family typewriter
+minY
+\family default
+,
+\family typewriter
+minZ
+\family default
+,
+\family typewriter
+maxX
+\family default
+,
+\family typewriter
+maxY
+\family default
+,
+\family typewriter
+maxZ
+\family default
+).
+ Finally, vary the tolerance for each nonlinear iteration (
+\family typewriter
+tolerance
+\family default
+ in the
+\family typewriter
+uzawa
+\family default
+ component).
+\end_layout
+
+\begin_layout Chapter
+Cookbooks
+\begin_inset LatexCommand \label{cha:Cookbooks}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Introduction
+\end_layout
+
+\begin_layout Standard
+In this chapter, you will edit a template file (
+\family typewriter
+input/cookbook/template.xml
+\family default
+) to create customized input files.
+ You should be able to use the template file as a basis for most of your
+ own input files.
+ There are two things in the template file, however, that might need modificatio
+n: the force of gravity, which by default is set to 1 (if you are using
+ cgs, for example, the force of gravity must be changed to 980), and the
+ normal velocities on all boundaries except the top, which are set to zero.
+ Beyond that, you only need to add where different materials are placed
+ initially.
+\end_layout
+
+\begin_layout Subsection
+Adding Lines to the Template File
+\end_layout
+
+\begin_layout Standard
+Unless otherwise specified, when you are instructed to add sections to the
+ input file
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+To copy and paste from this PDF with Adobe Acrobat, right click to get the
+ context menu and select ``Allow Hand Tool to Select Text.''
+\end_layout
+
+\end_inset
+
+, that text should be added after the line
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="components">
+\end_layout
+
+\begin_layout Standard
+at the beginning of the file, and before the lines
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<list name="plugins">
+\end_layout
+
+\begin_layout Standard
+The template file is already indented to prevent you from adding a component
+ in the middle of another component, although indentation is not critical.
+\end_layout
+
+\begin_layout Subsection
+Adding Variables to the Template File
+\end_layout
+
+\begin_layout Standard
+When you are instructed to add a variable, you must add it at the end of
+ the file before the closing line
+\end_layout
+
+\begin_layout LyX-Code
+</StGermainData>
+\end_layout
+
+\begin_layout Standard
+Finished versions of all of these examples are found in
+\family typewriter
+input/cookbook
+\family default
+.
+
+\end_layout
+
+\begin_layout Section
+\begin_inset LatexCommand \label{sec:Viscous-Material}
+
+\end_inset
+
+Viscous Material
+\end_layout
+
+\begin_layout Standard
+This example simply fills up the computational domain with a single viscous
+ material.
+ It is a valid input file, but will not run as nothing is moving.
+ This file mainly serves as the basis for subsequent examples.
+\end_layout
+
+\begin_layout Enumerate
+First, copy
+\family typewriter
+template.xml
+\family default
+ to
+\family typewriter
+myviscous.xml
+\family default
+ to edit as follows.
+
+\end_layout
+
+\begin_layout Enumerate
+Add in a material.
+ The simplest variety is a purely viscous material, so add a box covering
+ the whole domain:
+\end_layout
+
+\begin_deeper
+\begin_layout LyX-Code
+<struct name="boxShape">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">Box</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="startX">minX</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="endX">maxX</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="startY">minY</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="endY">maxY</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="startZ">minZ</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="endZ">maxZ</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout Standard
+Note: Default parameters for the box (e.g.,
+\family typewriter
+minX
+\family default
+,
+\family typewriter
+maxX
+\family default
+,
+\family typewriter
+minY
+\family default
+, etc.) are already defined in
+\family typewriter
+template.xml
+\family default
+.
+\end_layout
+
+\end_deeper
+\begin_layout Enumerate
+Then set the material's viscosity
+\end_layout
+
+\begin_deeper
+\begin_layout LyX-Code
+<struct name="backgroundViscosity">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">MaterialViscosity</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="eta0">1.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout Standard
+Remember that Gale has no internal knowledge of units, so if you think of
+ everything in cgs, then this implies a viscosity of
+\begin_inset Formula $1\frac{g}{cm^{2}\, s}$
+\end_inset
+
+.
+\end_layout
+
+\end_deeper
+\begin_layout Enumerate
+In order for Gale to include the viscosity in the output, we have to store
+ the viscosity in a separate field (see Section
+\begin_inset LatexCommand \ref{sub:StoreViscosity}
+
+\end_inset
+
+).
+\end_layout
+
+\begin_deeper
+\begin_layout LyX-Code
+<struct name="storeViscosity">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">StoreVisc</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="MaterialPointsSwarm">materialSwarm</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout Standard
+Here,
+\family typewriter
+materialswarm
+\family default
+ is a collection of particles.
+\end_layout
+
+\end_deeper
+\begin_layout Enumerate
+Finally, you create the material, using the components just created.
+\end_layout
+
+\begin_deeper
+\begin_layout LyX-Code
+<struct name="viscous">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">RheologyMaterial</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Shape">boxShape</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="density">1.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <list name="Rheology">
+\end_layout
+
+\begin_layout LyX-Code
+ <param>backgroundViscosity</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param>storeViscosity</param>
+\end_layout
+
+\begin_layout LyX-Code
+ </list>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\end_deeper
+\begin_layout Enumerate
+Save this file, as it will be the basis for other examples that follow.
+
+\end_layout
+
+\begin_layout Standard
+You can compare your result with the worked example in the file
+\family typewriter
+input/cookbook/viscous.xml
+\family default
+.
+\end_layout
+
+\begin_layout Section
+\begin_inset LatexCommand \label{sec:Viscous-Material-in}
+
+\end_inset
+
+Viscous Material in Simple Extension
+\end_layout
+
+\begin_layout Standard
+The input file you created in Section
+\begin_inset LatexCommand \ref{sec:Viscous-Material}
+
+\end_inset
+
+ is valid, but nothing moves, so Gale will output errors if you try to run
+ it.
+ In this next example, you will make the material extend by having the right
+ boundary move.
+\end_layout
+
+\begin_layout Enumerate
+Copy
+\family typewriter
+myviscous.xml
+\family default
+ to
+\family typewriter
+myviscous_extension.xml
+\family default
+.
+\end_layout
+
+\begin_layout Enumerate
+Make the right boundary move by changing the line after this section
+\end_layout
+
+\begin_deeper
+\begin_layout LyX-Code
+<param name="type">WallVC</param>
+\end_layout
+
+\begin_layout LyX-Code
+<param name="wall">right</param>
+\end_layout
+
+\begin_layout LyX-Code
+<list name="variables">
+\end_layout
+
+\begin_layout LyX-Code
+ <struct>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="name">vx</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="type">double</param>
+\end_layout
+
+\begin_layout Standard
+from
+\end_layout
+
+\begin_layout LyX-Code
+<param name="value">0.0</param>
+\end_layout
+
+\begin_layout Standard
+to
+\end_layout
+
+\begin_layout LyX-Code
+<param name="value">1.0</param>
+\end_layout
+
+\begin_layout Quote
+
+\series bold
+\color red
+Warning:
+\series default
+\color none
+ There are several
+\family typewriter
+WallVC
+\family default
+ structs:
+\family typewriter
+front
+\family default
+,
+\family typewriter
+back
+\family default
+,
+\family typewriter
+left
+\family default
+,
+\family typewriter
+right
+\family default
+,
+\family typewriter
+top
+\family default
+ and
+\family typewriter
+bottom
+\family default
+.
+ Here we have only modified the
+\family typewriter
+right
+\family default
+ side.
+\end_layout
+
+\end_deeper
+\begin_layout Enumerate
+You can now run this example, and the output will go into the directory
+
+\family typewriter
+output.template
+\family default
+.
+ If you want to run in 3D, you only need to change the line after
+\end_layout
+
+\begin_deeper
+\begin_layout LyX-Code
+<param name="outputPath">./output.template</param>
+\end_layout
+
+\begin_layout Standard
+from
+\end_layout
+
+\begin_layout LyX-Code
+<param name="dim">2</param>
+\end_layout
+
+\begin_layout Standard
+to
+\end_layout
+
+\begin_layout LyX-Code
+<param name="dim">3</param>
+\end_layout
+
+\end_deeper
+\begin_layout Standard
+A worked example is at
+\family typewriter
+input/cookbook/viscous_extension.xml
+\family default
+.
+ A visualization of the strain rate invariant and velocity (see Section
+
+\begin_inset LatexCommand \ref{sub:Visualization-with-ParaView}
+
+\end_inset
+
+) is shown in Figure
+\begin_inset LatexCommand \ref{fig:Strain-viscous-extension}
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Standard
+\begin_inset Graphics
+ filename ../../Gale/documentation/images/Paraview_viscous_extension.png
+ lyxscale 75
+ scale 75
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Caption
+\begin_inset LatexCommand \label{fig:Strain-viscous-extension}
+
+\end_inset
+
+Strain rate invariant and velocities of viscous material in extension
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The banding is a numerical artifact that arises from having a finite number
+ of particles per cell.
+ This example generates no topography, since the material is stretched uniformly.
+\end_layout
+
+\begin_layout Section
+Viscous Material with Complex Boundaries
+\end_layout
+
+\begin_layout Standard
+Another exercise is to make the bottom boundary move differently, and not
+ just have the material slide along.
+ In particular, this example will simulate a box like in Figure
+\begin_inset LatexCommand \ref{fig:Split-Boundary}
+
+\end_inset
+
+, where the bottom right side of the box moves, but the viscous material
+ sticks to the bottom left.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+placement h
+wide false
+sideways false
+status open
+
+\begin_layout Standard
+\align center
+\begin_inset Graphics
+ filename ../../Gale/documentation/images/splitwall.eps
+ width 80col%
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Caption
+\begin_inset LatexCommand \label{fig:Split-Boundary}
+
+\end_inset
+
+Split Boundary
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Enumerate
+First, copy
+\family typewriter
+myviscous_extension.xml
+\family default
+ to
+\family typewriter
+myviscous_split.xml
+\end_layout
+
+\begin_layout Enumerate
+Modify the bottom boundary condition of WallVC to
+\end_layout
+
+\begin_deeper
+\begin_layout LyX-Code
+<struct>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="type">WallVC</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="wall">bottom</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <list name="variables">
+\end_layout
+
+\begin_layout LyX-Code
+ <struct>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="name">vy</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="type">double</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="value">0.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+ </struct>
+\end_layout
+
+\begin_layout LyX-Code
+ <struct>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="name">vx</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="type">func</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="value">StepFunction</param>
+\end_layout
+
+\begin_layout LyX-Code
+ </struct>
+\end_layout
+
+\begin_layout LyX-Code
+ </list>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout Standard
+This makes the velocity of the bottom boundary a step function.
+
+\end_layout
+
+\end_deeper
+\begin_layout Enumerate
+You must also specify the parameters of the step function by adding the
+ variables
+\end_layout
+
+\begin_deeper
+\begin_layout LyX-Code
+<param name="StepFunctionLowerOffset">1.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+<param name="StepFunctionUpperOffset">1.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+<param name="StepFunctionValue">1.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+<param name="StepFunctionDim">0</param>
+\end_layout
+
+\begin_layout LyX-Code
+<param name="StepFunctionLessThan">False</param>
+\end_layout
+
+\begin_layout Standard
+to the end of the file (just before
+\family typewriter
+</StGermain
+\family default
+Data
+\family typewriter
+>
+\family default
+).
+
+\end_layout
+
+\begin_layout Quote
+
+\series bold
+\color red
+Warning:
+\series default
+\color none
+Do not add them in the list named
+\family typewriter
+``variables
+\family default
+.''
+\end_layout
+
+\end_deeper
+\begin_layout Standard
+A worked example is in the file
+\family typewriter
+input/cookbook/viscous_split.xml
+\family default
+.
+ A visualization of the strain rate invariant and velocity (see Section
+
+\begin_inset LatexCommand \ref{sub:Visualization-with-ParaView}
+
+\end_inset
+
+) shown in Figure
+\begin_inset LatexCommand \ref{fig:Strain-complex}
+
+\end_inset
+
+ shows that strain rate is concentrated around the step function in the
+ bottom velocity boundary.
+ Notice the development of a basin above the discontinuity.
+ The ability to track the development of topography on the free surfaces
+ is one of the strengths of Gale.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Standard
+\begin_inset Graphics
+ filename ../../Gale/documentation/images/Paraview_viscous_split.png
+ lyxscale 75
+ scale 75
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Caption
+\begin_inset LatexCommand \label{fig:Strain-complex}
+
+\end_inset
+
+Strain rate invariant and velocities with complex boundaries
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+\begin_inset LatexCommand \label{sec:Viscous-In-Outflow}
+
+\end_inset
+
+Viscous Material with Inflow/Outflow Boundaries
+\end_layout
+
+\begin_layout Standard
+This example implements a different kind of boundary condition, where material
+ flows in one side and out another as in Figure
+\begin_inset LatexCommand \ref{fig:Inflow/Outflow-Boundary}
+
+\end_inset
+
+.
+ The current example is not intended to be geologically realistic in any
+ sense, but is meant to illustrate the enormous flexibility we have in the
+ development of complex boundary conditions.
+ A more realistic model of subduction is included in the sample input file
+
+\family typewriter
+input/subduction.xml
+\family default
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+placement h
+wide false
+sideways false
+status open
+
+\begin_layout Standard
+\align center
+\begin_inset Graphics
+ filename ../../Gale/documentation/images/inflow.eps
+ width 80col%
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Caption
+\begin_inset LatexCommand \label{fig:Inflow/Outflow-Boundary}
+
+\end_inset
+
+Inflow/Outflow Boundary
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Enumerate
+Copy the file
+\family typewriter
+myviscous.xml
+\family default
+ that you created in Section
+\begin_inset LatexCommand \ref{sec:Viscous-Material}
+
+\end_inset
+
+ to
+\family typewriter
+myviscous_inflow.xml
+\family default
+.
+
+\end_layout
+
+\begin_layout Enumerate
+Then, add the following lines after the
+\family typewriter
+wrapTop
+\family default
+ line so that Gale keeps the left and bottom sides fixed:
+\end_layout
+
+\begin_deeper
+\begin_layout LyX-Code
+<param name="staticLeft">True</param>
+\end_layout
+
+\begin_layout LyX-Code
+<param name="staticBottom">True</param>
+\end_layout
+
+\end_deeper
+\begin_layout Enumerate
+Now specify the velocities on the boundaries using the
+\family typewriter
+StepFunctionProduct
+\family default
+ functions.
+ For the left boundary, modify the left
+\family typewriter
+WallVC
+\family default
+ to
+\end_layout
+
+\begin_deeper
+\begin_layout LyX-Code
+<param name="type">WallVC</param>
+\end_layout
+
+\begin_layout LyX-Code
+<param name="wall">left</param>
+\end_layout
+
+\begin_layout LyX-Code
+<list name="variables">
+\end_layout
+
+\begin_layout LyX-Code
+ <struct>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="name">vx</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="type">func</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="value">StepFunctionProduct3</param>
+\end_layout
+
+\begin_layout LyX-Code
+ </struct>
+\end_layout
+
+\begin_layout LyX-Code
+</list>
+\end_layout
+
+\begin_layout Standard
+and add the variables at the end of the file (just before
+\family typewriter
+</StGermainData>
+\family default
+)
+\end_layout
+
+\begin_layout LyX-Code
+<param name="StepFunctionProduct3Start">0.1</param>
+\end_layout
+
+\begin_layout LyX-Code
+<param name="StepFunctionProduct3End">0.2</param>
+\end_layout
+
+\begin_layout LyX-Code
+<param name="StepFunctionProduct3Value">1</param>
+\end_layout
+
+\end_deeper
+\begin_layout Enumerate
+For the bottom boundary, modify the bottom
+\family typewriter
+WallVC
+\family default
+ to
+\end_layout
+
+\begin_deeper
+\begin_layout LyX-Code
+<param name="type">WallVC</param>
+\end_layout
+
+\begin_layout LyX-Code
+<param name="wall">bottom</param>
+\end_layout
+
+\begin_layout LyX-Code
+<list name="variables">
+\end_layout
+
+\begin_layout LyX-Code
+ <struct>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="name">vy</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="type">func</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="value">StepFunctionProduct2</param>
+\end_layout
+
+\begin_layout LyX-Code
+ </struct>
+\end_layout
+
+\begin_layout LyX-Code
+ <struct>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="name">vx</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="type">func</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="value">StepFunctionProduct1</param>
+\end_layout
+
+\begin_layout LyX-Code
+ </struct>
+\end_layout
+
+\begin_layout LyX-Code
+</list>
+\end_layout
+
+\begin_layout Standard
+and add the variables to the end of the file (just before
+\family typewriter
+</StGermainData>
+\family default
+)
+\end_layout
+
+\begin_layout LyX-Code
+<param name="StepFunctionProduct1Start">0.9</param>
+\end_layout
+
+\begin_layout LyX-Code
+<param name="StepFunctionProduct1End">1.1</param>
+\end_layout
+
+\begin_layout LyX-Code
+<param name="StepFunctionProduct1Value">1.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+<param name="StepFunctionProduct2Start">0.9</param>
+\end_layout
+
+\begin_layout LyX-Code
+<param name="StepFunctionProduct2End">1.1</param>
+\end_layout
+
+\begin_layout LyX-Code
+<param name="StepFunctionProduct2Value">-1.0</param>
+\end_layout
+
+\end_deeper
+\begin_layout Enumerate
+Finally, you must alter the way that Gale creates particles.
+ The inflow boundary condition will naturally create a space devoid of particles.
+ Gale then creates new particles to fill that void.
+ Normally, Gale looks at nearby particles and replicates them.
+ However, nearby material has already changed a little from the boundary,
+ so replicating them will not give the new particles the correct properties.
+\end_layout
+
+\begin_deeper
+\begin_layout Standard
+To fix that, create a thin layer next to the boundary where material is
+ created anew.
+ To do that, first create this shape
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="leftBoundaryShape">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">Box</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="startX">minX</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="endX">0.1</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="startY">minY</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="endY">maxY</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="startZ">minZ</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="endZ">maxZ</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout Standard
+and then instruct the particle splitting routine to use this shape by adding
+
+\end_layout
+
+\begin_layout LyX-Code
+<param name="originalParticleShape">leftBoundaryShape</param>
+\end_layout
+
+\begin_layout Standard
+after
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="splittingRoutine">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">ReseedSplitting</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="idealParticleCount">particlesPerCell</param>
+\end_layout
+
+\end_deeper
+\begin_layout Standard
+A worked example is in the file
+\family typewriter
+input/cookbook/viscous_inflow.xml
+\family default
+.
+ A visualization of the strain rate invariant and velocity (see Section
+
+\begin_inset LatexCommand \ref{sub:Visualization-with-ParaView}
+
+\end_inset
+
+) is shown in Figure
+\begin_inset LatexCommand \ref{fig:Strain-inflow}
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Standard
+\begin_inset Graphics
+ filename ../../Gale/documentation/images/Paraview_viscous_inflow.png
+ lyxscale 75
+ scale 75
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Caption
+\begin_inset LatexCommand \label{fig:Strain-inflow}
+
+\end_inset
+
+Strain rate invariant and velocities with inflow/outflow boundaries
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Viscous Material with Stress Boundaries
+\end_layout
+
+\begin_layout Standard
+This example demonstrates yet another boundary condition, where only the
+ stress is specified at the boundary.
+ In particular, this example describes a box like Figure
+\begin_inset LatexCommand \ref{fig:Stress-Boundaries}
+
+\end_inset
+
+.
+ There is a tangential stress at the bottom causing a circulation, but otherwise
+ the bottom is stress-free.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Standard
+\align center
+\begin_inset Graphics
+ filename ../../Gale/documentation/images/stressbc.eps
+ width 80col%
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Caption
+\begin_inset LatexCommand \label{fig:Stress-Boundaries}
+
+\end_inset
+
+Stress Boundaries
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Enumerate
+Copy the file
+\family typewriter
+myviscous.xml
+\family default
+ that you created in Section
+\begin_inset LatexCommand \ref{sec:Viscous-Material}
+
+\end_inset
+
+ to
+\family typewriter
+myviscous_stressbc.xml
+\family default
+.
+
+\end_layout
+
+\begin_layout Enumerate
+Add a
+\family typewriter
+StressBC
+\family default
+ component
+\end_layout
+
+\begin_deeper
+\begin_layout LyX-Code
+<struct name="stressBC">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">StressBC</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="ForceVector">mom_force</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Swarm">picIntegrationPoints</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="wall">bottom</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="x_type">func</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="x_value">StepFunctionProduct1</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout Standard
+and corresponding variables to the end of the file (just before
+\family typewriter
+</StGermainData>
+\family default
+)
+\end_layout
+
+\begin_layout LyX-Code
+<param name="StepFunctionProduct1Start">0.9</param>
+\end_layout
+
+\begin_layout LyX-Code
+<param name="StepFunctionProduct1End">1.1</param>
+\end_layout
+
+\begin_layout LyX-Code
+<param name="StepFunctionProduct1Value">1.0</param>
+\end_layout
+
+\end_deeper
+\begin_layout Standard
+A worked example is in the file
+\family typewriter
+input/cookbook/viscous_stressbc.xml
+\family default
+.
+ A visualization of the strain rate invariant and velocity (see Section
+
+\begin_inset LatexCommand \ref{sub:Visualization-with-ParaView}
+
+\end_inset
+
+) is shown in Figure
+\begin_inset LatexCommand \ref{fig:Strain-stress}
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Standard
+\begin_inset Graphics
+ filename ../../Gale/documentation/images/Paraview_viscous_stressbc.png
+ lyxscale 75
+ scale 75
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Caption
+\begin_inset LatexCommand \label{fig:Strain-stress}
+
+\end_inset
+
+Strain rate invariant and velocities with stress boundaries
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+\begin_inset LatexCommand \label{sec:Viscous-Material-with}
+
+\end_inset
+
+Viscous Material with Initially Deformed Upper Boundary
+\end_layout
+
+\begin_layout Standard
+All of the previous examples are set up as a regular rectangular box.
+ However, Gale can also start with the top initially deformed, such as if
+ we had a mountain range with substantial topography.
+ This example will make it sinusoidal as in Figure
+\begin_inset LatexCommand \ref{fig:Sinusoidal-Top}
+
+\end_inset
+
+.
+ This example has no moving boundaries, so the material will simply relax.
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+placement h
+wide false
+sideways false
+status open
+
+\begin_layout Standard
+\align center
+\begin_inset Graphics
+ filename ../../Gale/documentation/images/sinusoid.eps
+ width 80col%
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Caption
+\begin_inset LatexCommand \label{fig:Sinusoidal-Top}
+
+\end_inset
+
+Sinusoidal Top
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Enumerate
+Copy
+\family typewriter
+myviscous.xml
+\family default
+ to
+\family typewriter
+myviscous_sinusoid.xml
+\family default
+.
+
+\end_layout
+
+\begin_layout Enumerate
+Add a
+\family typewriter
+SurfaceAdaptor
+\family default
+ component:
+\end_layout
+
+\begin_deeper
+\begin_layout LyX-Code
+<struct name="surfaceAdaptor">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">SurfaceAdaptor</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="mesh">mesh-linear</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="sourceGenerator">linearMesh-generator</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="surfaceType">sine</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <list name="origin">
+\end_layout
+
+\begin_layout LyX-Code
+ <param>0.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+ </list>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="amplitude">0.1</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="frequency">6.28318530718</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\end_deeper
+\begin_layout Standard
+A worked example is in
+\family typewriter
+input/cookbook/viscous_sinusoid.xml
+\family default
+.
+ A visualization of the strain rate invariant and velocity (see Section
+
+\begin_inset LatexCommand \ref{sub:Visualization-with-ParaView}
+
+\end_inset
+
+) is shown in
+\begin_inset LatexCommand \ref{fig:Strain-initial-deformed}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Standard
+\begin_inset Graphics
+ filename ../../Gale/documentation/images/Paraview_viscous_sinusoid.png
+ lyxscale 75
+ scale 75
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Caption
+\begin_inset LatexCommand \label{fig:Strain-initial-deformed}
+
+\end_inset
+
+Strain rate invariant and velocities with initially deformed upper boundary
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Multiple Viscous Materials
+\end_layout
+
+\begin_layout Standard
+All of the previous examples have only one type of viscous material.
+ This example will create a simulation where there are multiple viscous
+ materials such as in Figure
+\begin_inset LatexCommand \ref{fig:Multiple-Viscous-Materials}
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+placement h
+wide false
+sideways false
+status open
+
+\begin_layout Standard
+\align center
+\begin_inset Graphics
+ filename ../../Gale/documentation/images/multi-material.eps
+ width 80col%
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Caption
+\begin_inset LatexCommand \label{fig:Multiple-Viscous-Materials}
+
+\end_inset
+
+Multiple Viscous Materials
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Enumerate
+Copy
+\family typewriter
+myviscous_extension.xml
+\family default
+ (see Section
+\begin_inset LatexCommand \ref{sec:Viscous-Material-in}
+
+\end_inset
+
+) to
+\family typewriter
+mymulti_material.xml
+\family default
+.
+
+\end_layout
+
+\begin_layout Enumerate
+Add the sphere.
+\end_layout
+
+\begin_deeper
+\begin_layout LyX-Code
+<struct name="sphereShape">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">Sphere</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="CentreX">1.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="CentreY">0.15</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="radius">0.10</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout Standard
+Note: If run in 3D, this is a sphere.
+ The example shown here is run in 2D, so the result is a circle.
+\end_layout
+
+\end_deeper
+\begin_layout Enumerate
+Then add the new material.
+\end_layout
+
+\begin_deeper
+\begin_layout LyX-Code
+<struct name="sphereViscosity">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">MaterialViscosity</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="eta0">10.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="sphereViscous">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">RheologyMaterial</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Shape">sphereShape</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="density">1.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <list name="Rheology">
+\end_layout
+
+\begin_layout LyX-Code
+ <param>sphereViscosity</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param>storeViscosity</param>
+\end_layout
+
+\begin_layout LyX-Code
+ </list>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\end_deeper
+\begin_layout Enumerate
+Change the shape of the original material so it is not inside the sphere.
+ To do this, create a new shape which is the old shape minus the sphere:
+\end_layout
+
+\begin_deeper
+\begin_layout LyX-Code
+<struct name="nonSphereShape">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">Intersection</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <list name="shapes">
+\end_layout
+
+\begin_layout LyX-Code
+ <param>boxShape</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param>!sphereShape</param>
+\end_layout
+
+\begin_layout LyX-Code
+ </list>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\end_deeper
+\begin_layout Enumerate
+Finally, modify the original viscous material to use this new
+\family typewriter
+nonSphereShape
+\family default
+ by changing the line after
+\end_layout
+
+\begin_deeper
+\begin_layout LyX-Code
+<struct name="viscous">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">RheologyMaterial</param>
+\end_layout
+
+\begin_layout Standard
+from
+\end_layout
+
+\begin_layout LyX-Code
+<param name="Shape">boxShape</param>
+\end_layout
+
+\begin_layout Standard
+to
+\end_layout
+
+\begin_layout LyX-Code
+<param name="Shape">nonSphereShape</param>
+\end_layout
+
+\end_deeper
+\begin_layout Standard
+A worked example is in
+\family typewriter
+input/cookbook/multi_material.xml
+\family default
+.
+ A visualization of the strain rate invariant and velocity (see Section
+
+\begin_inset LatexCommand \ref{sub:Visualization-with-ParaView}
+
+\end_inset
+
+) is shown in Figure
+\begin_inset LatexCommand \ref{fig:Strain-multiple}
+
+\end_inset
+
+,
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Standard
+\begin_inset Graphics
+ filename ../../Gale/documentation/images/Paraview_multi_material.png
+ lyxscale 75
+ scale 75
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Caption
+\begin_inset LatexCommand \label{fig:Strain-multiple}
+
+\end_inset
+
+Strain rate invariant and velocities with multiple viscous materials
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+and the viscosity of the particles is shown in Figure
+\begin_inset LatexCommand \ref{fig:Viscosities-with-multiple}
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Standard
+\begin_inset Graphics
+ filename ../../Gale/documentation/images/Paraview_multi_viscosity.png
+ lyxscale 75
+ scale 75
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Caption
+\begin_inset LatexCommand \label{fig:Viscosities-with-multiple}
+
+\end_inset
+
+Viscosities with multiple viscous materials
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Yielding Material in Simple Extension
+\end_layout
+
+\begin_layout Standard
+This example replaces the background viscous material with a yielding material.
+ This will produce localizations as some material fails.
+\end_layout
+
+\begin_layout Enumerate
+Copy
+\family typewriter
+mymulti_material.xml
+\family default
+ to
+\family typewriter
+myyielding.xml
+\end_layout
+
+\begin_layout Enumerate
+Add a
+\family typewriter
+StrainWeakening
+\family default
+ component and a
+\family typewriter
+MohrCoulomb
+\family default
+ component
+\end_layout
+
+\begin_deeper
+\begin_layout LyX-Code
+<struct name="strainWeakening">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">StrainWeakening</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="TimeIntegrator">timeIntegrator</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="MaterialPointsSwarm">materialSwarm</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="softeningStrain">0.1</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="initialDamageFraction">0.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="initialDamageWavenumber">0.5</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="initialDamageFactor">0.5</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="healingRate">0.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="yielding">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">MohrCoulomb</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="PressureField">PressureField</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="VelocityGradientsField">VelocityGradientsField</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="MaterialPointsSwarm">materialSwarm</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Context">context</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="StrainWeakening">strainWeakening</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="cohesion">1.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="cohesionAfterSoftening">0.0001</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="frictionCoefficient">0.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="frictionCoefficientAfterSoftening">0.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="minimumYieldStress">0.00001</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\end_deeper
+\begin_layout Enumerate
+Finally, remove the existing viscous
+\family typewriter
+RheologyMaterial
+\end_layout
+
+\begin_deeper
+\begin_layout LyX-Code
+<struct name="viscous">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">RheologyMaterial</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Shape">nonSphereShape</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="density">1.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <list name="Rheology">
+\end_layout
+
+\begin_layout LyX-Code
+ <param>backgroundViscosity</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param>storeViscosity</param>
+\end_layout
+
+\begin_layout LyX-Code
+ </list>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout Standard
+and replace it with a yielding
+\family typewriter
+RheologyMaterial
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="crust">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">RheologyMaterial</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Shape">nonSphereShape</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <list name="Rheology">
+\end_layout
+
+\begin_layout LyX-Code
+ <param>backgroundViscosity</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param>yielding</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param>storeViscosity</param>
+\end_layout
+
+\begin_layout LyX-Code
+ </list>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\end_deeper
+\begin_layout Standard
+A worked example is in
+\family typewriter
+input/cookbook/yielding.xml
+\family default
+.
+ A visualization of the strain rate invariant and velocity (see Section
+
+\begin_inset LatexCommand \ref{sub:Visualization-with-ParaView}
+
+\end_inset
+
+) is shown in Figure
+\begin_inset LatexCommand \ref{fig:strain-yield}
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Standard
+\begin_inset Graphics
+ filename ../../Gale/documentation/images/Paraview_yielding.png
+ lyxscale 75
+ scale 75
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Caption
+\begin_inset LatexCommand \label{fig:strain-yield}
+
+\end_inset
+
+Strain rate invariant and velocities of yielding material in extension
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+A visualization of the viscosity of the particles is shown in Figure
+\begin_inset LatexCommand \ref{fig:Viscosity-of-yielding}
+
+\end_inset
+
+,
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Standard
+\begin_inset Graphics
+ filename ../../Gale/documentation/images/Paraview_yielding_viscosity.png
+ lyxscale 75
+ scale 75
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Caption
+\begin_inset LatexCommand \label{fig:Viscosity-of-yielding}
+
+\end_inset
+
+Viscosity of yielding material in extension
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+and a visualization of the yielding of the particles is shown in Figure
+
+\begin_inset LatexCommand \ref{fig:Degree-of-yielding}
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Standard
+\begin_inset Graphics
+ filename ../../Gale/documentation/images/Paraview_yielding_yielding.png
+ lyxscale 75
+ scale 75
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Caption
+\begin_inset LatexCommand \label{fig:Degree-of-yielding}
+
+\end_inset
+
+Degree of yielding of yielding material in extension
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Chapter
+Modifying Gale
+\begin_inset LatexCommand \label{cha:Modifying-Gale}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Introduction
+\end_layout
+
+\begin_layout Standard
+If you wish to change material properties, here is a brief overview of how
+ to modify the code.
+ The following is currently lacking in many areas, but will be expanded
+ and refined in future releases.
+
+\end_layout
+
+\begin_layout Section
+Software Components of Gale
+\end_layout
+
+\begin_layout Standard
+Gale makes use of several physics libraries, including StGermain, StgFEM,
+ PiCellerator, and UnderWorld.
+ These are proven, capable, open-source finite element method libraries
+ written by the Victorian Partnership for Advanced Computing (VPAC) and
+ Louis Moresi's group at Monash University (see Fig
+\begin_inset LatexCommand \ref{fig:Mapping-between-MicroFEM}
+
+\end_inset
+
+).
+ Gale also makes use of PETSc, a suite of data structures and routines for
+ the parallel solution of scientific applications modeled by partial differentia
+l equations.
+
+\end_layout
+
+\begin_layout Subsection
+StGermain
+\end_layout
+
+\begin_layout Standard
+StGermain provides an infrastructure that can be used to create reusable,
+ collaborative computational development environments.
+ It aims to provide the efficiency and style of coding near that of traditional
+ HPC as well as new techniques and methods in scientific computing.
+ Effectively, it is the application of contemporary software engineering
+ on multi-disciplinary computational research.
+ In particular, StGermain can be used in the development of computational
+ finite element codes.
+ It permits the interchanging of numerical schemes without having to change
+ the problem description or the constitutive rules utilized.
+ It also allows numerical schemes and constitutive rules to be reused for
+ different problems in different disciplines.
+ Scientists can then switch to new computational technologies as they become
+ available.
+ StGermain also capitalizes on the resources invested in software development
+ on a research project, rendering that software effectively reusable for
+ subsequent projects.
+ In turn, intellectual property, skills and adaptability of the recipients
+ develop over time.
+
+\begin_inset LatexCommand \htmlurl[StGermain Web Site]{csd.vpac.org/twiki/bin/view/Stgermain/WebHome}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+PETSc
+\end_layout
+
+\begin_layout Standard
+PETSc, the Portable, Extensible Toolkit for Scientific Computation, is a
+ suite of data structures and routines for the uni- and parallel-processor
+ solution of large-scale scientific application problems modeled by partial
+ differential equations.
+ It employs the MPI standard for all message-passing communication.
+
+\begin_inset LatexCommand \htmlurl[PETSc Web Site]{www-unix.mcs.anl.gov/petsc/petsc-as/}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float figure
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Caption
+\begin_inset LatexCommand \label{fig:Mapping-between-MicroFEM}
+
+\end_inset
+
+Mapping between MicroFEM and Gale
+\end_layout
+
+\begin_layout LyX-Code
+
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Graphics
+ filename ../../Gale/documentation/images/GALE_imag.eps
+ lyxscale 80
+ scale 80
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+StgFEM
+\end_layout
+
+\begin_layout Standard
+StgFEM uses the StGermain philosophy of reusability and collaborative developmen
+t to create a finite element problem composer in terms of both the linear
+ system to be solved and the finite element discretization of the problem
+ domain.
+ The composition can be described in XML and could be represented in a network
+ diagram with an appropriate tool.
+ StgFEM describes finite element systems for various formulations in a manner
+ that can allow the underlying numerics to be interchanged.
+
+\begin_inset LatexCommand \htmlurl[StgFEM Web Site]{csd.vpac.org/twiki/bin/view/Stgfem/WebHome}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+PiCellerator
+\end_layout
+
+\begin_layout Standard
+PICellerator (Particle In Cellerator), a Lagrangian Integration Point Finite
+ Element framework, is implemented as an integration scheme substitute for
+ the default Gaussian scheme implemented in StgFEM.
+ The PICellerator concept has since grown to become a general Lagrangian
+ integration scheme framework and a Lagrangian constitutive rule framework.
+ The PIC scheme is provided and other Arbitrary Lagrangian Eulerian schemes
+ are in development.
+ Constitutive rules are reusable across these schemes.
+
+\begin_inset LatexCommand \htmlurl[PICellerator Web Site]{csd.vpac.org/twiki/bin/view/PICellerator/WebHome}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+UnderWorld
+\end_layout
+
+\begin_layout Standard
+UnderWorld is a StGermain parallel modeling framework Geoscience research
+ code which utilizes a Lagrangian particle-in-cell finite element scheme
+ (the prototype of which is the Ellipsis code), visualised using gLucifer.
+ UnderWorld (Monash University), StGermain (Victorian Partnership for Advanced
+ Computing or VPAC) and gLucifer (Monash University) are under development
+ as part of the Australian Computational Earth Systems Simulator (ACcESS),
+ an Australian Government National Research Facility, a node of which is
+ located at the Australian Crustal Research Centre (ACRC) at Monash University
+ (Clayton Campus).
+
+\begin_inset LatexCommand \htmlurl[UnderWorld Web Site]{wasabi.maths.monash.edu.au/twiki/view/Software/Underworld}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+System Description
+\end_layout
+
+\begin_layout Standard
+Gale uses StgFEM to formulate implicit finite element systems, with the
+ bulk of the information placed in a stiffness matrix and a force vector.
+ Depending on the type of solver used, there may be several matrices and
+ vectors.
+ The stiffness matrix class has a member whose purpose is to assemble the
+ entire matrix.
+ It does this through the use of
+\begin_inset Quotes eld
+\end_inset
+
+stiffness matrix terms.
+\begin_inset Quotes erd
+\end_inset
+
+ The
+\family typewriter
+StiffnessMatrixTerm
+\family default
+ class provides an interface through which the elemental contributions to
+ the matrix may be influenced.
+ In typical fluid flow systems, the majority of the physics is applied to
+ the model through constitutive laws which modify the stiffness matrix to
+ reflect certain physical situations.
+ The
+\family typewriter
+ConstitutiveMatrix
+\family default
+ class inherits from
+\family typewriter
+StiffnessMatrixTerm
+\family default
+, providing an interface tailored to implementing material-based continuum
+ physics.
+
+\end_layout
+
+\begin_layout Standard
+So, where does the actual physics take place? The answer is in the Rheology
+ class, but first look at the PIC (particle in cell) scheme.
+ There are a number of benefits to using a PIC scheme, but the main use
+ is to store material properties on each particle.
+ These properties can then be used to drive our constitutive laws, in turn
+ modifying the produced stiffness matrices.
+ For each defined material in the domain, there may be a number of associated
+ rheological laws.
+ Whenever an element in the system is assembled, each stiffness matrix term
+ is evaluated, implying that the constitutive matrix will be evaluated for
+ each element.
+ For each particle internal to an element, the
+\family typewriter
+ConstitutiveMatrix
+\family default
+ class will evaluate all associated rheologies, each rheology modifying
+ the constitutive matrix.
+
+\end_layout
+
+\begin_layout Standard
+Modifying the constitutive matrix takes place in the form of viscosity values.
+ In this, probably the simplest of rheological laws, the
+\family typewriter
+ModifyConstitutiveMatrix
+\family default
+ method simply sets a specific viscosity value for the current element/material
+ point tuple.
+
+\end_layout
+
+\begin_layout Section
+Sample Rheologies
+\end_layout
+
+\begin_layout Subsection
+Simple Viscous
+\end_layout
+
+\begin_layout Standard
+This excerpt is taken from the file
+\family typewriter
+src/Underworld/Rheology/src/MaterialViscosity.c
+\family default
+.
+ It has been inherited from the Rheology class and thus possesses a virtual
+ method named
+\end_layout
+
+\begin_layout LyX-Code
+
+\family typewriter
+MaterialViscosity_ModifyConstitutiveMatrix
+\family default
+
+\end_layout
+
+\begin_layout Standard
+which has been overridden to set the viscosity in the constitutive matrix,
+ as follows:
+\end_layout
+
+\begin_layout LyX-Code
+void _MaterialViscosity_ModifyConstitutiveMatrix(
+\end_layout
+
+\begin_layout LyX-Code
+ void* rheology,
+\end_layout
+
+\begin_layout LyX-Code
+ ConstitutiveMatrix* constitutiveMatrix,
+\end_layout
+
+\begin_layout LyX-Code
+ MaterialPointsSwarm* swarm,
+\end_layout
+
+\begin_layout LyX-Code
+ Element_LocalIndex lElement_I,
+\end_layout
+
+\begin_layout LyX-Code
+ MaterialPoint* materialPoint,
+\end_layout
+
+\begin_layout LyX-Code
+ Coord xi )
+\end_layout
+
+\begin_layout LyX-Code
+{
+\end_layout
+
+\begin_layout LyX-Code
+ MaterialViscosity* self = (MaterialViscosity*)rheology;
+\end_layout
+
+\begin_layout LyX-Code
+ ConstitutiveMatrix_SetIsotropicViscosity( constitutiveMatrix,
+\end_layout
+
+\begin_layout LyX-Code
+ self->eta0 );
+\end_layout
+
+\begin_layout LyX-Code
+}
+\end_layout
+
+\begin_layout Standard
+The parameters passed to this method provide access to the rheology class's
+ members/methods, the constitutive matrix, the swarm (material points),
+ the index of the element currently being assembled, the material point
+ currently being evaluated, and the material point's elemental coordinates.
+\end_layout
+
+\begin_layout Chapter
+\start_of_appendix
+Input File Format
+\begin_inset LatexCommand \label{cha:Input-File-Format}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Structure
+\end_layout
+
+\begin_layout Standard
+The input files are XML files.
+ This leverages a well known format to specify concepts like hierarchies,
+ lists, parameters, and arbitrary structures.
+ The entire document is placed withing a
+\family typewriter
+StGermainData
+\family default
+ structure.
+\end_layout
+
+\begin_layout LyX-Code
+<?xml version="1.0"?>
+\end_layout
+
+\begin_layout LyX-Code
+<StGermainData xmlns="http://www.vpac.org/StGermain/XML_IO_Handler/Jun2003">
+\end_layout
+
+\begin_layout LyX-Code
+...
+\end_layout
+
+\begin_layout LyX-Code
+</StGermainData>
+\end_layout
+
+\begin_layout Standard
+Within that structure, there are five main parts of every Gale input file:
+ the components, the plugins, EulerDeform, Velocity Conditions, and the
+ variables.
+\end_layout
+
+\begin_layout Subsection
+Components
+\begin_inset LatexCommand \label{sub:Components}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The components section is separated off from the rest of the file with an
+ enclosing
+\family typewriter
+components
+\family default
+ structure.
+ This
+\family typewriter
+components
+\family default
+ structure is where the bulk of the file will be.
+ It specifies things like what the mesh will be like, which material goes
+ where, what the material properties are, what kind of solver to use, etc.
+ Most of the ideas you need to specify your problem will go into the components.
+ When adding a new component, it is important to remember to put the new
+ component inside the components structure.
+ Otherwise Gale will (silently) not use that component.
+ For example, an input file such as
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="components">
+\end_layout
+
+\begin_layout LyX-Code
+ <struct name="conditionFunctions">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">StgFEM_StandardConditionFunctions</param>
+\end_layout
+
+\begin_layout LyX-Code
+ </struct>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout Standard
+will correctly initialize
+\family typewriter
+StgFEM_StandardConditionFunctions
+\family default
+, but the input file
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="components">
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="conditionFunctions">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">StgFEM_StandardConditionFunctions</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout Standard
+will not.
+\end_layout
+
+\begin_layout Subsection
+Plugins
+\begin_inset LatexCommand \label{sub:Plugins}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Gale also has the ability to load modules during runtime.
+ To use these plugins, simply list them in a section outside of the
+\family typewriter
+components
+\family default
+ structure.
+ For example, the following lines will enable the
+\family typewriter
+DumpSwarm
+\family default
+,
+\family typewriter
+EulerDeform
+\family default
+,and
+\family typewriter
+VTKOutput
+\family default
+ plugins
+\end_layout
+
+\begin_layout LyX-Code
+<list name="plugins">
+\end_layout
+
+\begin_layout LyX-Code
+ <param>Underworld_EulerDeform</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param>Underworld_DumpSwarm</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param>Underworld_VTKOutput</param>
+\end_layout
+
+\begin_layout LyX-Code
+</list>
+\end_layout
+
+\begin_layout Standard
+Dynamically loading modules is, in general, difficult to get working on
+ multiple platforms.
+ To make things easier, Gale is bundled with a number of plugins compiled
+ into the code and ready to use:
+\end_layout
+
+\begin_layout LyX-Code
+StgFEM_FrequentOutput
+\end_layout
+
+\begin_layout LyX-Code
+StgFEM_CPUTime
+\end_layout
+
+\begin_layout LyX-Code
+Underworld_MovingMesh
+\end_layout
+
+\begin_layout LyX-Code
+Underworld_Vrms
+\end_layout
+
+\begin_layout LyX-Code
+Underworld_EulerDeform
+\end_layout
+
+\begin_layout LyX-Code
+StgFEM_PrintFeVariableDiscreteValues
+\end_layout
+
+\begin_layout LyX-Code
+Underworld_DumpSwarm
+\end_layout
+
+\begin_layout LyX-Code
+Underworld_VTKOutput
+\end_layout
+
+\begin_layout Standard
+Note that you must still include those plugins in the list of plugins in
+ order to use them.
+ You can add additional plugins by modifying the list of static plugins
+ in
+\family typewriter
+src/Gale/src/main.c
+\family default
+ and making sure that the plugin is compiled into the Gale executable.
+\end_layout
+
+\begin_layout Standard
+If you want to use dynamically loaded plugins, make sure that you compiled
+ with shared libraries (use the
+\family typewriter
+--with-shared
+\family default
+ option when compiling) and set your
+\family typewriter
+LD_LIBRARY_PATH
+\family default
+environment variable appropriately.
+\end_layout
+
+\begin_layout Subsection
+EulerDeform
+\begin_inset LatexCommand \label{sub:EulerDeform}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The
+\family typewriter
+Underworld_EulerDeform
+\family default
+ component allows the upper surface to move freely or stay rigidly in place.
+ An example
+\family typewriter
+EulerDeform
+\family default
+ struct is
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="EulerDeform">
+\end_layout
+
+\begin_layout LyX-Code
+ <list name="systems">
+\end_layout
+
+\begin_layout LyX-Code
+ <struct>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="mesh">mesh-constant</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="remesher">pressureRemesher</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="velocityField">VelocityField</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <list name="fields">
+\end_layout
+
+\begin_layout LyX-Code
+ <struct>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="field">PressureField</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="variable">pressure</param>
+\end_layout
+
+\begin_layout LyX-Code
+ </struct>
+\end_layout
+
+\begin_layout LyX-Code
+ </list>
+\end_layout
+
+\begin_layout LyX-Code
+ </struct>
+\end_layout
+
+\begin_layout LyX-Code
+ <struct>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="mesh">mesh-linear</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="remesher">velocityRemesher</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="velocityField">VelocityField</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="wrapTop">True</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <list name="fields">
+\end_layout
+
+\begin_layout LyX-Code
+ <struct>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="field">VelocityField</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="variable">velocity</param>
+\end_layout
+
+\begin_layout LyX-Code
+ </struct>
+\end_layout
+
+\begin_layout LyX-Code
+ </list>
+\end_layout
+
+\begin_layout LyX-Code
+ </struct>
+\end_layout
+
+\begin_layout LyX-Code
+ </list>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout Standard
+This tells Gale to remesh both the pressure and velocity field.
+ The components
+\family typewriter
+\size small
+pressureRemesher
+\family default
+,
+\family typewriter
+velocityRemesher
+\family default
+,
+\family typewriter
+pressureField
+\family default
+,
+\family typewriter
+velocityField
+\family default
+,
+\family typewriter
+pressure
+\family default
+\size default
+, and
+\size small
+
+\family typewriter
+velocity
+\family default
+\size default
+ all must be defined earlier (see Section
+\begin_inset LatexCommand \ref{sub:Components}
+
+\end_inset
+
+).
+
+\end_layout
+
+\begin_layout Standard
+Note the critical line
+\end_layout
+
+\begin_layout LyX-Code
+<param name="wrapTop">True</param>
+\end_layout
+
+\begin_layout Standard
+that tells Gale to make the top surface conform to the simulation.
+ Other options (
+\family typewriter
+wrapBottom
+\family default
+,
+\family typewriter
+wrapLeft
+\family default
+) are available, but untested.
+
+\end_layout
+
+\begin_layout Standard
+Additionally, Gale can fix the positions of the boundaries.
+ For example, if you are running a shortening model, normally Gale will
+ move the boundaries inward as the simulation progresses.
+ If different parts of the boundary are moving at different rates (such
+ as if you were simulating one slab sliding over the other), then the side
+ boundary would quickly become distorted and ruin the simulation.
+ To fix the right boundary, set the variable
+\family typewriter
+staticRight
+\family default
+ to
+\family typewriter
+True
+\end_layout
+
+\begin_layout LyX-Code
+<param name="staticRight">True</param>
+\end_layout
+
+\begin_layout Standard
+Similarly, you can independently set the left, top, bottom, front, and back
+ boundaries.
+\end_layout
+
+\begin_layout Standard
+Note that you must include
+\family typewriter
+Underworld_EulerDeform
+\family default
+ in the list of plugins (see Section
+\begin_inset LatexCommand \ref{sub:Plugins}
+
+\end_inset
+
+) in order for this section to have any effect.
+\end_layout
+
+\begin_layout Subsection
+Velocity Boundary Conditions
+\end_layout
+
+\begin_layout Standard
+This section specifies what the boundary conditions on the velocity will
+ be.
+ See Section
+\begin_inset LatexCommand \ref{sub:Velocity-Boundary-Conditions}
+
+\end_inset
+
+ for more details.
+\end_layout
+
+\begin_layout Subsection
+Variables
+\begin_inset LatexCommand \label{sub:Variables}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The last section is where most of our numeric constants are placed.
+ For example, how many time steps, how often to print output, etc.
+ You may also declare variables for convenience (e.g., the number of grid
+ points) and use it elsewhere, such as in the components.
+ If you are using the basic set of components, then the more important parameter
+s are:
+\end_layout
+
+\begin_layout Description
+maxTimeSteps The number of time steps to take in the simulation.
+ Each time step can cover a different amount of time.
+ Gale determines how big of a step to take by dividing the grid size by
+ the largest velocity during that time step.
+ Unfortunately, there is no way to stop at a maximum time.
+\end_layout
+
+\begin_layout Description
+dumpEvery How often DumpSwarm dumps information to files.
+\end_layout
+
+\begin_layout Description
+checkPointEvery How often to dump every variable to files.
+\end_layout
+
+\begin_layout Description
+outputPath The directory to put output files in.
+\end_layout
+
+\begin_layout Description
+dim The number of dimensions of the problem (2 or 3).
+\end_layout
+
+\begin_layout Description
+minX,minY,minZ,maxX,maxY,maxZ The physical size of the box you are simulating.
+ Note that this may be modified by
+\family typewriter
+SurfaceAdaptor
+\family default
+ (Section
+\begin_inset LatexCommand \ref{sec:Deformed-Upper-Boundary}
+
+\end_inset
+
+).
+\end_layout
+
+\begin_layout Description
+elementResI,elementResJ,elementResK The number of elements in each direction.
+ Note that the number of grid points is one larger (e.g., 64 elements -> 65
+ grid points).
+\end_layout
+
+\begin_layout Description
+shadowDepth When running in parallel, every parameter only computes quantities
+ over a portion of the grid.
+ To do this, each processor must keep copies of points that belong to other
+ processors.
+ This parameter specifies how wide the region of copied points is.
+ You should never need to change this from 1.
+\end_layout
+
+\begin_layout Description
+gaussParticlesX,gaussParticlesY,gaussParticlesZ The number of particles
+ in each direction when putting down particles using a Gaussian distribution.
+ You should never need to change this number.
+\end_layout
+
+\begin_layout Description
+particlesPerCell The ideal number of particles in each element.
+ Gale will attempt to keep the number of particles in each element close
+ to this number.
+ You need to vary this number to gauge how sensitive the results of our
+ simulation are to this number.
+\end_layout
+
+\begin_layout Section
+Basic Components
+\begin_inset LatexCommand \label{sec:Basic-Components}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Gale is built on top of StGermain, which is a very general framework for
+ scientific computation.
+ Because StGermain is so general, you have to tell it fairly basic things
+ that would be implicit in most codes.
+ For example, you must tell StGermain that you want to set up a regular
+ mesh and solve a finite element problem on it.
+ This means you have to include a number of components in every input file.
+ These components are
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="mesh-constant">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">FeMesh</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="elementType">constant</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="constantMesh-generator">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">C0Generator</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="mesh">mesh-constant</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="elementMesh">mesh-linear</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="mesh-linear">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">FeMesh</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="elementType">linear</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="linearMesh-generator">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">CartesianGenerator</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="mesh">mesh-linear</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="dim">dim</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="shadowDepth">shadowDepth</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <list name="size">
+\end_layout
+
+\begin_layout LyX-Code
+ <param>elementResI</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param>elementResJ</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param>elementResK</param>
+\end_layout
+
+\begin_layout LyX-Code
+ </list>
+\end_layout
+
+\begin_layout LyX-Code
+ <list name="minCoord">
+\end_layout
+
+\begin_layout LyX-Code
+ <param>minX</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param>minY</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param>minZ</param>
+\end_layout
+
+\begin_layout LyX-Code
+ </list>
+\end_layout
+
+\begin_layout LyX-Code
+ <list name="maxCoord">
+\end_layout
+
+\begin_layout LyX-Code
+ <param>maxX</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param>maxY</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param>maxZ</param>
+\end_layout
+
+\begin_layout LyX-Code
+ </list>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="velocity">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">MeshVariable</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="mesh">mesh-linear</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Rank">Vector</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="DataType">Double</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="VectorComponentCount">dim</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <list name="names">
+\end_layout
+
+\begin_layout LyX-Code
+ <param>vx</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param>vy</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param>vz</param>
+\end_layout
+
+\begin_layout LyX-Code
+ </list>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="velocityBCs">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">CompositeVC</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Data">mesh-linear</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="velocityICs">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">CompositeVC</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Data">mesh-linear</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="velocityDofLayout">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">DofLayout</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="mesh">mesh-linear</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="BaseVariableCount">dim</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <list name="BaseVariables">
+\end_layout
+
+\begin_layout LyX-Code
+ <param>vx</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param>vy</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param>vz</param>
+\end_layout
+
+\begin_layout LyX-Code
+ </list>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="VelocityField">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">FeVariable</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="FEMesh">mesh-linear</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="DofLayout">velocityDofLayout</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="BC">velocityBCs</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="IC">velocityICs</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="LinkedDofInfo">velocityLinkedDofs</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="VelocityMagnitudeField">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">OperatorFeVariable</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Operator">Magnitude</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="FeVariable">VelocityField</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="VelocityGradientsField">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">OperatorFeVariable</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Operator">Gradient</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="FeVariable">VelocityField</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="VelocityGradientsInvariantField">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">OperatorFeVariable</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Operator">TensorInvariant</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="FeVariable">VelocityGradientsField</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="VelocityXXField">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">OperatorFeVariable</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Operator">TakeFirstComponent</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="FeVariable">VelocityField</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="VelocityYYField">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">OperatorFeVariable</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Operator">TakeSecondComponent</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="FeVariable">VelocityField</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="StrainRateField">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">OperatorFeVariable</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Operator">TensorSymmetricPart</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="FeVariable">VelocityGradientsField</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="VorticityField">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">OperatorFeVariable</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Operator">TensorAntisymmetricPart</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="FeVariable">VelocityGradientsField</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="StrainRateInvariantField">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">OperatorFeVariable</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Operator">SymmetricTensor_Invariant</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="FeVariable">StrainRateField</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="StrainRateXXField">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">OperatorFeVariable</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Operator">TakeFirstComponent</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="FeVariable">StrainRateField</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="StrainRateYYField">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">OperatorFeVariable</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Operator">TakeSecondComponent</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="FeVariable">StrainRateField</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="pressure">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">MeshVariable</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="mesh">mesh-constant</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Rank">Scalar</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="DataType">Double</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="pressureDofLayout">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">DofLayout</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="mesh">mesh-constant</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <list name="BaseVariables">
+\end_layout
+
+\begin_layout LyX-Code
+ <param>pressure</param>
+\end_layout
+
+\begin_layout LyX-Code
+ </list>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="PressureField">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">FeVariable</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="FEMesh">mesh-constant</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="DofLayout">pressureDofLayout</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="LinkedDofInfo">pressureLinkedDofs</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="cellLayout">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">SingleCellLayout</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="particleLayout">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">GaussParticleLayout</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="gaussSwarm">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">IntegrationPointsSwarm</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="CellLayout">cellLayout</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="ParticleLayout">particleLayout</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="FeMesh">mesh-linear</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="TimeIntegrator">timeIntegrator</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="IntegrationPointMapper">gaussMapper</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="gaussMapper">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">GaussMapper</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="IntegrationPointsSwarm">gaussSwarm</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="MaterialPointsSwarm">gaussMaterialSwarm</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="backgroundLayout">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">BackgroundParticleLayout</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="gaussMaterialSwarm">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">MaterialPointsSwarm</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="CellLayout">cellLayout</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="ParticleLayout">backgroundLayout</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="FeMesh">mesh-linear</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="timeIntegrator">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">TimeIntegrator</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="order">1</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="simultaneous">t</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Context">context</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="elementCellLayout">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">ElementCellLayout</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Mesh">mesh-linear</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="weights">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">PCDVC</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="resolutionX">10</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="resolutionY">10</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="resolutionZ">10</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="lowerT">0.6</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="upperT">25</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="maxDeletions">3</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="maxSplits">3</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="MaterialPointsSwarm">materialSwarm</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="localLayout">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">MappedParticleLayout</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="picIntegrationPoints">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">IntegrationPointsSwarm</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="CellLayout">elementCellLayout</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="ParticleLayout">localLayout</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="FeMesh">mesh-linear</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="WeightsCalculator">weights</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="TimeIntegrator">timeIntegrator</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="IntegrationPointMapper">mapper</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="mapper">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">CoincidentMapper</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="IntegrationPointsSwarm">picIntegrationPoints</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="MaterialPointsSwarm">materialSwarm</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="materialSwarmParticleLayout">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">MeshParticleLayout</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="mesh">mesh-linear</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="cellParticleCount">particlesPerCell</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="materialSwarm">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">MaterialPointsSwarm</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="CellLayout">elementCellLayout</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="ParticleLayout">materialSwarmParticleLayout</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="FeMesh">mesh-linear</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="SplittingRoutine">splittingRoutine</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="RemovalRoutine">removalRoutine</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="EscapedRoutine">escapedRoutine</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="materialSwarmAdvector">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">SwarmAdvector</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Swarm">materialSwarm</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="TimeIntegrator">timeIntegrator</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="VelocityField">VelocityField</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="PeriodicBCsManager">periodicBCsManager</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="allowFallbackToFirstOrder">True</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="splittingRoutine">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">ReseedSplitting</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="idealParticleCount">particlesPerCell</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="solutionVelocity">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">SolutionVector</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="FeVariable">VelocityField</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="solutionPressure">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">SolutionVector</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="FeVariable">PressureField</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="mom_force">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">ForceVector</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="FeVariable">VelocityField</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="ExtraInfo">context</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="cont_force">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">ForceVector</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="FeVariable">PressureField</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="ExtraInfo">context</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="k_matrix">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">StiffnessMatrix</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="RowVariable">VelocityField</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="ColumnVariable">VelocityField</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="RHS">mom_force</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="allowZeroElementContributions">False</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="constitutiveMatrix">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">ConstitutiveMatrixCartesian</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Swarm">picIntegrationPoints</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="StiffnessMatrix">k_matrix</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="g_matrix">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">StiffnessMatrix</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="RowVariable">VelocityField</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="ColumnVariable">PressureField</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="RHS">cont_force</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="allowZeroElementContributions">False</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="gradientStiffnessMatrixTerm">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">GradientStiffnessMatrixTerm</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Swarm">gaussSwarm</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="StiffnessMatrix">g_matrix</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="preconditioner">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">StiffnessMatrix</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="RowVariable">PressureField</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="ColumnVariable">PressureField</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="RHS">cont_force</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="allowZeroElementContributions">True</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="preconditionerTerm">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">UzawaPreconditionerTerm</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Swarm">picIntegrationPoints</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="StiffnessMatrix">preconditioner</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="uzawa">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">Stokes_SLE_UzawaSolver</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Preconditioner">preconditioner</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="tolerance">1.0e-5</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="maxIterations">5000</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="stokesEqn">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">Stokes_SLE</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="SLE_Solver">uzawa</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Context">context</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="StressTensorMatrix">k_matrix</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="GradientMatrix">g_matrix</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="DivergenceMatrix"></param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="CompressibilityMatrix">c_matrix</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="VelocityVector">solutionVelocity</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="PressureVector">solutionPressure</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="ForceVector">mom_force</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="ContinuityForceVector">cont_force</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="killNonConvergent">false</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="nonLinearMaxIterations">nonLinearMaxIterations</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="nonLinearTolerance">nonLinearTolerance</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="makeConvergenceFile">false</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="background">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">Everywhere</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="escapedRoutine">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">EscapedRoutine</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="idealParticleCount">0</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="velocityRemesher">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">StripRemesher</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="mesh">mesh-linear</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="meshType">regular</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <list name="dim">
+\end_layout
+
+\begin_layout LyX-Code
+ <param>true</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param>true</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param>true</param>
+\end_layout
+
+\begin_layout LyX-Code
+ </list>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="pressureRemesher">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">CellRemesher</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="mesh">mesh-constant</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="meshType">regular</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="dim">3</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="cellMesh">mesh-linear</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+
+\end_layout
+
+\begin_layout Standard
+For almost all simulations, you will not need to change these components.
+\end_layout
+
+\begin_layout Section
+Shapes
+\begin_inset LatexCommand \label{sec:Shapes}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+When setting up a simulation, Gale reads in shapes to determine what to
+ put where.
+ For example, you can create a simulation with different materials by creating
+ different shapes and putting different materials in them.
+ As a simple example, you can create a 3D box
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="simpleBox">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">Box</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="startX">0.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="endX">1.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="startY">0.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="endY">1.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="startZ">0.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="endZ">1.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout Standard
+You can perform operations on shapes to create new shapes.
+ For example, if you also create a sphere
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="simpleSphere">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">Sphere</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="radius">1.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout Standard
+then you can compose it with the box to create a new shape
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="nonSphere">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">Intersection</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <list name="shapes">
+\end_layout
+
+\begin_layout LyX-Code
+ <param>simpleBox</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param>!simpleSphere</param>
+\end_layout
+
+\begin_layout LyX-Code
+ </list>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout Standard
+Note that the exclamation point ``!'' in front of
+\family typewriter
+simpleSphere
+\family default
+ means ``not.'' So
+\family typewriter
+Intersection
+\family default
+ creates a shape that is the intersection of the box and everywhere outside
+ of the sphere.
+ You can list an arbitrary number of shapes in
+\family typewriter
+Intersection
+\family default
+.
+ Also, you can use
+\family typewriter
+Union
+\family default
+ to create a shape that covers all of the input shapes.
+\end_layout
+
+\begin_layout Standard
+In addition, every shape accepts the translation variables
+\family typewriter
+CentreX
+\family default
+,
+\family typewriter
+CentreY
+\family default
+, and
+\family typewriter
+CentreZ
+\family default
+, and the Euler angles
+\family typewriter
+alpha
+\family default
+,
+\family typewriter
+beta
+\family default
+, and
+\family typewriter
+gamma
+\family default
+.
+ So if you modify the Box example above to
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="simpleBox">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">Box</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="CentreX">1.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="startX">0.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="endX">1.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="startY">0.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="endY">1.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="startZ">0.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="endZ">1.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout Standard
+then the box will actually span from 1 to 2.
+\end_layout
+
+\begin_layout Standard
+The Euler angles use the
+\begin_inset Formula $y$
+\end_inset
+
+ convention, first rotating about the original
+\begin_inset Formula $z$
+\end_inset
+
+ axis an angle
+\begin_inset Formula $\gamma$
+\end_inset
+
+, then rotating around the new
+\begin_inset Formula $y$
+\end_inset
+
+ axis an angle
+\begin_inset Formula $\beta$
+\end_inset
+
+, and finally a rotation around the new
+\begin_inset Formula $z$
+\end_inset
+
+ axis an angle
+\begin_inset Formula $\alpha$
+\end_inset
+
+.
+ Specifically, these rotations are expressed through the rotation matrix
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \[
+R=\left(\begin{array}{ccc}
+-\sin\alpha\sin\gamma+\cos\alpha\cos\beta\cos\gamma & \sin\alpha\cos\gamma+\cos\beta\sin\gamma\cos\alpha & -\cos\alpha\sin\beta\\
+-\cos\alpha\sin\gamma-\cos\beta\cos\gamma\sin\alpha & \cos\alpha\cos\gamma-\cos\beta\sin\gamma\sin\alpha & \sin\alpha\sin\beta\\
+\sin\beta\cos\alpha & \sin\beta\sin\alpha & \cos\beta\end{array}\right).\]
+
+\end_inset
+
+ So when Gale is trying to figure out whether a coordinate
+\begin_inset Formula $(x,y,z)$
+\end_inset
+
+ is inside a shape, it creates a new coordinate
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \[
+\left(\begin{array}{c}
+x'\\
+y'\\
+z'\end{array}\right)=\left(\left(\begin{array}{c}
+x\\
+y\\
+z\end{array}\right)-\left(\begin{array}{c}
+CentreX\\
+CentreY\\
+CentreZ\end{array}\right)\right)R,\]
+
+\end_inset
+
+ which it uses in the formulas below.
+\end_layout
+
+\begin_layout Standard
+Finally, you may tell Gale to invert the shape with the
+\family typewriter
+invert
+\family default
+ variable, making the inside the outside and vice versa.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+<lyxtabular version="3" rows="8" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Defaults
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+CentreX
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+CentreY
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+CentreZ
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+alpha
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+beta
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+gamma
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+invert
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+False
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+BelowCosinePlane
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \[
+y<offset+delta*\cos\left(\frac{\pi period}{180}*x+phase\right)\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Defaults
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+offset
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+delta
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0.5
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+period
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+1
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+phase
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\newline
+
+\newline
+See also the notes for BelowPlane.
+\end_layout
+
+\begin_layout Subsection
+BelowPlane
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \[
+y<offset\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+This shape also uses the variables
+\begin_inset Formula $minX$
+\end_inset
+
+,
+\begin_inset Formula $minY$
+\end_inset
+
+,
+\begin_inset Formula $minZ$
+\end_inset
+
+,
+\begin_inset Formula $maxX$
+\end_inset
+
+,
+\begin_inset Formula $maxY$
+\end_inset
+
+, and
+\begin_inset Formula $maxZ$
+\end_inset
+
+, which are only used when computing the volume of this shape.
+\newline
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+<lyxtabular version="3" rows="8" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Defaults
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+offset
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+minX
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+minY
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+minZ
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+maxX
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+1
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+maxY
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+1
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+maxZ
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+1
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Box
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \[
+\begin{array}{c}
+startX<x<endX\\
+startY<y<endY\\
+startZ<z<endZ\end{array}\]
+
+\end_inset
+
+Alternately, you can use widths, in which case
+\begin_inset Formula \[
+\begin{array}{c}
+|x|<widthX/2\\
+|y|<widthY/2\\
+|z|<widthZ/2\end{array}.\]
+
+\end_inset
+
+You may mix and match these specification (e.g., use start/end for
+\begin_inset Formula $x$
+\end_inset
+
+, and width for
+\begin_inset Formula $y$
+\end_inset
+
+).
+ If both are specified for one coordinate, Gale will use start and end.
+
+\newline
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Defaults
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+widthX
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+widthY
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+widthZ
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+ConvexHull
+\end_layout
+
+\begin_layout Standard
+This shape is a convenience function for creating intersections of
+\family typewriter
+BelowPlane
+\family default
+.
+ The input is a list of vertices.
+ From each vertex, Gale computes a vector and plane normal to this vector.
+ The half spaces below the planes are then intersected to create a shape.
+ At present, you may only use three vertices in 2D, and four vertices in
+ 3D.
+ As an example, the shape
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="triangleShape">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">ConvexHull</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <list name="verticies">
+\end_layout
+
+\begin_layout LyX-Code
+ <asciidata>
+\end_layout
+
+\begin_layout LyX-Code
+ <columnDefinition name = "x" type="double"/>
+\end_layout
+
+\begin_layout LyX-Code
+ <columnDefinition name = "y" type="double"/>
+\end_layout
+
+\begin_layout LyX-Code
+ 1.0 1.0
+\end_layout
+
+\begin_layout LyX-Code
+ -1.0 1.0
+\end_layout
+
+\begin_layout LyX-Code
+ 0.0 -1.0
+\end_layout
+
+\begin_layout LyX-Code
+ </asciidata>
+\end_layout
+
+\begin_layout LyX-Code
+ </list>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout Standard
+creates a shape with vertices at (0,2), (4,-2), (-4,-2).
+\end_layout
+
+\begin_layout Subsection
+Cylinder
+\end_layout
+
+\begin_layout Standard
+This shape uses a variable
+\begin_inset Formula $perpendicularAxis$
+\end_inset
+
+ to determine which direction is perpendicular to the axis of the cylinder.
+ This variable accepts any of (x, y, z, X, Y, Z, i, j, k, I, J, K, 0, 1,
+ 2).
+ For the case where
+\begin_inset Formula $perpendicularAxis=z$
+\end_inset
+
+, then
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \[
+\begin{array}{c}
+radius^{2}>x^{2}+y^{2}\\
+startX<x<endX\\
+startY<y<endY\\
+startZ<z<endZ\end{array}.\]
+
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="8" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Defaults
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+radius
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+startX
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $-\infty$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+startY
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $-\infty$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+startZ
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $-\infty$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+endX
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\infty$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+endY
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\infty$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+endZ
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\infty$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Everywhere
+\end_layout
+
+\begin_layout Standard
+This is a convenience shape simply meaning everywhere.
+\end_layout
+
+\begin_layout Subsection
+PolygonShape
+\end_layout
+
+\begin_layout Standard
+This is primarily a two-dimensional shape.
+ The input to this shape is a list of vertices.
+ To figure out whether a point is inside the polygon, Gale adds up all of
+ the angles of the vectors going to the vertices.
+ If the point is inside the polygon, then the angles will sum to
+\begin_inset Formula $\pm2\pi$
+\end_inset
+
+, depending on the direction you specify vertices.
+ If the point is outside the polygon, then the angles sum to 0.
+ A simple example is a triangle
+\end_layout
+
+\begin_layout LyX-Code
+ <struct name="triangleShape">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">PolygonShape</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <list name="verticies">
+\end_layout
+
+\begin_layout LyX-Code
+ <asciidata>
+\end_layout
+
+\begin_layout LyX-Code
+ <columnDefinition name = "x" type="double"/>
+\end_layout
+
+\begin_layout LyX-Code
+ <columnDefinition name = "y" type="double"/>
+\end_layout
+
+\begin_layout LyX-Code
+ 0.0 0.0
+\end_layout
+
+\begin_layout LyX-Code
+ 1.0 0.0
+\end_layout
+
+\begin_layout LyX-Code
+ 1.0 1.0
+\end_layout
+
+\begin_layout LyX-Code
+ </asciidata>
+\end_layout
+
+\begin_layout LyX-Code
+ </list>
+\end_layout
+
+\begin_layout LyX-Code
+ </struct>
+\end_layout
+
+\begin_layout Standard
+This creates a triangle with vertices at (0,0), (1,0), (1,1).
+\end_layout
+
+\begin_layout Standard
+You can extrude this shape into three dimensions by specifying startZ and
+ endZ.
+\newline
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Defaults
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+startZ
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+endZ
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Sphere
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \[
+x^{2}+y^{2}+z^{2}<radius^{2}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Defaults
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+radius
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Superellipsoid
+\end_layout
+
+\begin_layout Standard
+In two dimensions
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \[
+\left(\frac{x}{radiusX}\right)^{2/epsilon1}+\left(\frac{y}{radiusY}\right)^{2/epsilon1}<1,\]
+
+\end_inset
+
+and in three dimensions
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \[
+\left(\left(\frac{x}{radiusX}\right)^{2/epsilon2}+\left(\frac{y}{radiusY}\right)^{2/epsilon2}\right)^{epsilon2/epsilon1}+\left(\frac{z}{radiusZ}\right)^{2/epsilon1}<1.\]
+
+\end_inset
+
+
+\newline
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+<lyxtabular version="3" rows="6" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Defaults
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+radiusX
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+1
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+radiusY
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+1
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+radiusZ
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+1
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+epsilon1
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+1
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+epsilon2
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+1
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Materials
+\begin_inset LatexCommand \label{sec:Materials}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Gale supports two kinds of rheologies: viscous and yielding.
+ You can combine these two rheologies to create a more realistic composite
+ rheology.
+ You then pair this composite rheology with a shape to actually lay down
+ material on the grid.
+ As a simple example, you can create a viscous rheology
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="viscousRheology">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">MaterialViscosity</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="eta0">10.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout Standard
+and a Von Mises yielding rheology
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="strainWeakening">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">StrainWeakening</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="TimeIntegrator">timeIntegrator</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="MaterialPointsSwarm">materialSwarm</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="softeningStrain">0.1</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="initialDamageFraction">0.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="initialDamageWavenumber">0.5</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="initialDamageFactor">0.5</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="healingRate">0.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\newline
+
+\newline
+<struct name="yieldingRheology">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">VonMises</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="cohesion">10.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="cohesionAfterSoftening">1.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout Standard
+and combine them together with
+\family typewriter
+materialShape
+\family default
+ (see Section
+\begin_inset LatexCommand \ref{sec:Shapes}
+
+\end_inset
+
+ on how to create shapes)
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="yieldingMaterial">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">RheologyMaterial</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Shape">yieldingShape</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <list name="Rheology">
+\end_layout
+
+\begin_layout LyX-Code
+ <param>viscousRheology</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param>yieldingRheology</param>
+\end_layout
+
+\begin_layout LyX-Code
+ </list>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout Standard
+To output the effective isotropic viscosity, you have to add a
+\family typewriter
+StoreVisc
+\family default
+ component
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="storeViscosity">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">StoreVisc</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="MaterialPointsSwarm">materialSwarm</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout Standard
+and then add that to the material
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="yieldingMaterial">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">RheologyMaterial</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Shape">yieldingShape</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <list name="Rheology">
+\end_layout
+
+\begin_layout LyX-Code
+ <param>storeViscosity</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param>viscousRheology</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param>yieldingRheology</param>
+\end_layout
+
+\begin_layout LyX-Code
+ </list>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout Subsection
+StoreVisc
+\begin_inset LatexCommand \label{sub:StoreViscosity}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+This is not a rheology per se, but rather it is an extra field where Gale
+ saves the effective isotropic viscosity.
+ For pure viscous materials, this will be the same as the viscosity you
+ supply.
+ For yielding rheologies, the effective viscosity will change as the particle
+ yields.
+ This component needs a
+\family typewriter
+MaterialPointsSwarm
+\family default
+, which in all of the sample input files is called
+\family typewriter
+materialSwarm
+\family default
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Defaults
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+MaterialPointsSwarm
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+1
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Viscous
+\end_layout
+
+\begin_layout Subsubsection
+MaterialViscosity
+\end_layout
+
+\begin_layout Standard
+This is the simplest rheology.
+ There is only one variable, the viscosity
+\family typewriter
+eta0
+\family default
+.
+\newline
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Defaults
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+eta0
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+1
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsubsection
+Frank-Kamenetskii
+\end_layout
+
+\begin_layout Standard
+This is a temperature-dependent viscosity
+\begin_inset Formula \[
+eta=eta0*\exp\left(-theta*T\right).\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Defaults
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+eta0
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+1
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+theta
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Yielding
+\end_layout
+
+\begin_layout Standard
+Yielding rheologies are a bit more complicated.
+
+\end_layout
+
+\begin_layout Subsubsection
+StrainWeakening
+\end_layout
+
+\begin_layout Standard
+First you need to create a
+\family typewriter
+StrainWeakening
+\family default
+ component.
+
+\family typewriter
+StrainWeakening
+\family default
+ is mainly used to define an initial distribution of strain in a material
+ and to calculate the accumulated strain on each particle.
+ To that end, it requires a number of parameters.
+\end_layout
+
+\begin_layout Description
+TimeIntegrator This is the component used for time integration to accumulate
+ strain.
+ Given the standard components in Section
+\begin_inset LatexCommand \ref{sec:Basic-Components}
+
+\end_inset
+
+, this will be
+\family typewriter
+timeIntegrator
+\family default
+.
+\end_layout
+
+\begin_layout Description
+MaterialPointsSwarm This is the swarm of particles that this rheology will
+ tie itself to.
+ Given the standard components in Section
+\begin_inset LatexCommand \ref{sec:Basic-Components}
+
+\end_inset
+
+, this will be
+\family typewriter
+materialSwarm
+\family default
+.
+\end_layout
+
+\begin_layout Description
+healingRate With this parameter, accumulated strain can decrease.
+ Specifically, the time derivative of accumulated strain becomes
+\begin_inset Formula \[
+\frac{\sigma_{yield}}{\eta}\left(\frac{\beta}{1-\beta}-healingRate\right),\]
+
+\end_inset
+
+ where
+\begin_inset Formula $\beta\equiv\sigma_{yield}/\sigma$
+\end_inset
+
+,
+\begin_inset Formula $\sigma_{yield}$
+\end_inset
+
+ is the yield stress,
+\begin_inset Formula $\sigma$
+\end_inset
+
+ is some measure of the current stress (e.g., the second invariant of the
+ stress tensor), and
+\begin_inset Formula $\eta$
+\end_inset
+
+ is the isotropic viscosity.
+ Note that the healing rate should be between 0 and 1.
+\end_layout
+
+\begin_layout Description
+softeningStrain The strain at which the material has fully yielded.
+\end_layout
+
+\begin_layout Description
+initialDamageFraction The chance that an individual material particle will
+ have a non-zero initial strain.
+\end_layout
+
+\begin_layout Description
+initialDamageWaveNumber The wavenumber for the initial random strain.
+ To avoid having initial strain on the edges of the box, this should be
+ set to the inverse of the horizontal length of the box.
+\end_layout
+
+\begin_layout Description
+initialDamageFactor The maximum initial random strain for a particle is
+\newline
+
+\family typewriter
+initialDamageFactor
+\family default
+*
+\family typewriter
+softeningStrain
+\family default
+.
+
+\end_layout
+
+\begin_layout Description
+randomSeed A random number seed used when computing which particles are
+ initially strained.
+\end_layout
+
+\begin_layout Description
+initialStrainShape If defined, the initial random strain will only occur
+ within this shape (outside the shape the initial random strain will be
+ zero).
+\end_layout
+
+\begin_layout Standard
+You can also define a strain weakening ratio
+\begin_inset Formula $\alpha\equiv\min\left(1,\gamma/\gamma_{softening}\right)$
+\end_inset
+
+, where
+\begin_inset Formula $\gamma$
+\end_inset
+
+ is the accumulated strain, and
+\begin_inset Formula $\gamma_{softening}$
+\end_inset
+
+ is the softening strain.
+ This allows us to define quantities like the effective cohesion
+\begin_inset Formula $C_{effective}\equiv C_{pristine}\left(1-\alpha\right)+C_{yielded}\alpha$
+\end_inset
+
+ and effective friction coefficient
+\begin_inset Formula $\phi_{effective}=\phi_{pristine}\left(1-\alpha\right)+\phi_{yielded}\alpha$
+\end_inset
+
+.
+\newline
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+<lyxtabular version="3" rows="10" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Defaults
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+TimeIntegrator
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+none
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+MaterialPointsSwarm
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+none
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+healingRate
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+softeningStrain
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\infty$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+initialDamageFraction
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+initialDamageWaveNumber
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+-1.0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+initialDamageFactor
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+1.0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+randomSeed
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+initialStrainShape
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+none
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsubsection
+\begin_inset LatexCommand \label{sub:VonMises}
+
+\end_inset
+
+VonMises
+\end_layout
+
+\begin_layout Standard
+This is the simplest yielding rheology in Gale.
+ The yielding stress is simply the effective cohesion, so this rheology
+ only has a few input parameters:
+\end_layout
+
+\begin_layout Itemize
+
+\family typewriter
+cohesion
+\family default
+ and
+\family typewriter
+cohesionAfterSoftening
+\family default
+ have the obvious meanings.
+
+\end_layout
+
+\begin_layout Itemize
+
+\family typewriter
+minimumYieldStress
+\family default
+ sets an absolute minimum to the stress required to make the material yield.
+\end_layout
+
+\begin_layout Itemize
+
+\family typewriter
+StrainRateSoftening
+\family default
+ is a Boolean variable that changes how the constitutive matrix is modified
+ when the material has yielded.
+ If
+\family typewriter
+StrainRateSoftening
+\family default
+ is
+\family typewriter
+True
+\family default
+, then the viscosity is set to
+\begin_inset Formula \[
+\eta_{effective}=2\sigma_{yield}^{2}\eta/\left(\sigma_{yield}^{2}+I_{2}^{2}\right),\]
+
+\end_inset
+
+ where
+\begin_inset Formula $I_{2}$
+\end_inset
+
+ is the second invariant of the stress tensor.
+ Otherwise the viscosity is set to
+\end_layout
+
+\begin_deeper
+\begin_layout Standard
+\begin_inset Formula \[
+\eta_{effective}=\eta\sigma_{yield}/I_{2},\]
+
+\end_inset
+
+ which essentially sets the stress of the particle to the yield stress.
+\newline
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Defaults
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+cohesion
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+cohesionAfterSoftening
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+minimumYieldStress
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+StrainRateSoftening
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+False
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\end_deeper
+\begin_layout Subsubsection
+DruckerPrager
+\end_layout
+
+\begin_layout Standard
+This rheology uses the same parameters as Von Mises, but also adds a friction
+ coefficient that can soften.
+ Specifically, the yield stress becomes
+\begin_inset Formula \[
+\sigma_{yield}=\alpha p+C_{p},\]
+
+\end_inset
+
+where
+\begin_inset Formula \[
+\begin{array}{ccc}
+C_{p} & = & \frac{6C_{effective}\cos\phi_{effective}}{\sqrt{3}\left(3-\sin\phi_{effective}\right)}\\
+\alpha & = & \frac{6\sin\phi_{effective}}{\sqrt{3}\left(3-\sin\phi_{effective}\right)}\end{array},\]
+
+\end_inset
+
+and
+\begin_inset Formula $p$
+\end_inset
+
+ is the pressure.
+
+\newline
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Defaults
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+frictionCoefficient
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+frictionCoefficientAfterSoftening
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\newline
+
+\end_layout
+
+\begin_layout Standard
+(See also
+\begin_inset LatexCommand \ref{sub:VonMises}
+
+\end_inset
+
+.)
+\end_layout
+
+\begin_layout Subsubsection
+MohrCoulomb
+\end_layout
+
+\begin_layout Standard
+This rheology is like Drucker-Prager, but it uses the actual normal stress
+ instead of inferring a normal stress from the pressure.
+ More explicitly, the yield shear stress is
+\begin_inset Formula \[
+\sigma_{yield}=\sigma_{n}\tan\phi_{effective}+C_{effective}.\]
+
+\end_inset
+
+ When the material is yielding, the viscosity is modified so that the stress
+ on the particle is the yield stress.
+\newline
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+<lyxtabular version="3" rows="6" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Defaults
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+cohesion
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+cohesionAfterSoftening
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+frictionCoefficient
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+frictionCoefficientAfterSoftening
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+minimumYieldStress
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsubsection
+FaultingMoresiMulhaus2006
+\end_layout
+
+\begin_layout Standard
+This is a fairly complicated non-isotropic rheology.
+ The full details can be found in Moresi and Mülhaus (2006)
+\begin_inset LatexCommand \cite{Moresi faulting}
+
+\end_inset
+
+, but essentially it keeps track of which direction a material is strained.
+ To do so, it uses a component called
+\family typewriter
+Director
+\family default
+.
+ For the standard components given in Section
+\begin_inset LatexCommand \ref{sec:Basic-Components}
+
+\end_inset
+
+, this would be
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="director">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">Director</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="TimeIntegrator">timeIntegrator</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="VelocityGradientsField">VelocityGradientsField</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="MaterialPointsSwarm">materialSwarm</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="initialDirectionX">0.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="initialDirectionY">1.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="initialDirectionZ">0.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="dontUpdate">True</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout Standard
+Otherwise, it adds one variable not present in
+\family typewriter
+MohrCoulomb
+\family default
+:
+\family typewriter
+ignoreOldOrientation
+\family default
+.
+ This tells Gale whether it should check to see whether material will weaken
+ further in the current direction, or if it should try every direction equally
+ each time step.
+\newline
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+<lyxtabular version="3" rows="7" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Defaults
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+cohesion
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+cohesionAfterSoftening
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+frictionCoefficient
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+frictionCoefficientAfterSoftening
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+minimumYieldStress
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+ignoreOldOrientation
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+False
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Boundary Conditions
+\end_layout
+
+\begin_layout Standard
+Gale's computational domain is logically Eulerian.
+ So in 2D, there are four boundaries:
+\family typewriter
+right
+\family default
+,
+\family typewriter
+left
+\family default
+,
+\family typewriter
+top
+\family default
+, and
+\family typewriter
+bottom
+\family default
+.
+ 3D adds
+\family typewriter
+front
+\family default
+ and
+\family typewriter
+back
+\family default
+.
+ Note that the boundaries in the
+\begin_inset Formula $z$
+\end_inset
+
+ axis are
+\family typewriter
+front
+\family default
+ and
+\family typewriter
+back
+\family default
+, not
+\family typewriter
+top
+\family default
+ and
+\family typewriter
+bottom
+\family default
+.
+ In many cases, this makes it simple to switch between 2D and 3D.
+ When doing this, you may ignore the warning that the
+\begin_inset Formula $z$
+\end_inset
+
+ boundaries are empty in 2D.
+\end_layout
+
+\begin_layout Subsection
+Velocity Boundary Conditions
+\begin_inset LatexCommand \label{sub:Velocity-Boundary-Conditions}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To impose boundary conditions on the velocity, add a composite variable
+ condition (CompositeVC) to the input file.
+ Within that CompositeVC, add a list of conditions.
+ Within each condition, specify which boundary and what the velocity's value
+ is.
+ For example, to set the
+\begin_inset Formula $y$
+\end_inset
+
+ velocity on the bottom to zero, add
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="velocityBCs">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="type">CompositeVC</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <list name="vcList">
+\end_layout
+
+\begin_layout LyX-Code
+ <struct>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="type">WallVC</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="wall">bottom</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <list name="variables">
+\end_layout
+
+\begin_layout LyX-Code
+ <struct>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="name">vy</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="type">double</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="value">0</param>
+\end_layout
+
+\begin_layout LyX-Code
+ </struct>
+\end_layout
+
+\begin_layout LyX-Code
+ </list>
+\end_layout
+
+\begin_layout LyX-Code
+ </struct>
+\end_layout
+
+\begin_layout LyX-Code
+ </list>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout Standard
+If, instead, you set
+\family typewriter
+vy
+\family default
+ to a non-zero value, then the boundary will move as the simulation proceeds.
+ If you want the sides to remain fixed, then you probably want flux boundaries,
+ in which case you will also have to specify a few more things (see Section
+
+\begin_inset LatexCommand \ref{sub:Flux-Boundary-Conditions}
+
+\end_inset
+
+).
+\end_layout
+
+\begin_layout Standard
+You can also set the velocity to a function.
+ For example, to also set the
+\begin_inset Formula $x$
+\end_inset
+
+ velocity to have a Gaussian distribution
+\begin_inset Formula $\exp\left(-\left(\frac{x-0.5}{0.1}\right)^{2}\right)$
+\end_inset
+
+
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="velocityBCs">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="type">CompositeVC</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <list name="vcList">
+\end_layout
+
+\begin_layout LyX-Code
+ <struct>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="type">WallVC</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="wall">bottom</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <list name="variables">
+\end_layout
+
+\begin_layout LyX-Code
+ <struct>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="name">vy</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="type">double</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="value">0</param>
+\end_layout
+
+\begin_layout LyX-Code
+ </struct>
+\end_layout
+
+\begin_layout LyX-Code
+ <struct>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="name">vx</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="type">func</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="value">Gaussian</param>
+\end_layout
+
+\begin_layout LyX-Code
+ </struct>
+\end_layout
+
+\begin_layout LyX-Code
+ </list>
+\end_layout
+
+\begin_layout LyX-Code
+ </struct>
+\end_layout
+
+\begin_layout LyX-Code
+ </list>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<param name="GaussianHeight">1.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+<param name="GaussianWidth">0.1</param>
+\end_layout
+
+\begin_layout LyX-Code
+<param name="GaussianCenter">0.5</param>
+\end_layout
+
+\begin_layout LyX-Code
+<param name="GaussianDim">0</param>
+\end_layout
+
+\begin_layout Standard
+Note that the parameters are separated out into the variables section (see
+ Section
+\begin_inset LatexCommand \ref{sub:Variables}
+
+\end_inset
+
+).
+ In general, you can use any of the Standard Condition Functions (see Section
+
+\begin_inset LatexCommand \ref{sec:Standard-Condition-Functions}
+
+\end_inset
+
+) to specify the velocities.
+\end_layout
+
+\begin_layout Subsection
+Flux Boundary Conditions
+\begin_inset LatexCommand \label{sub:Flux-Boundary-Conditions}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Sometimes, you may wish to have material flow across the boundary instead
+ of having the boundary move.
+ A simple example would be like Figure
+\begin_inset LatexCommand \ref{fig:General-subduction-model}
+
+\end_inset
+
+, where material flows in from the left and out through the bottom.
+ There are three things that you must specify for this to work.
+\end_layout
+
+\begin_layout Enumerate
+
+\series bold
+The boundaries do not move.
+
+\series default
+For the slab subduction model, you need to ensure that neither the bottom
+ nor left boundaries move.
+ Do this by specifying
+\end_layout
+
+\begin_deeper
+\begin_layout LyX-Code
+
+\family typewriter
+<param name="staticBottom">True</param>
+\newline
+<param name="staticLeft">True</param>
+\end_layout
+
+\begin_layout Standard
+in EulerDeform (see Section
+\begin_inset LatexCommand \ref{sub:EulerDeform}
+
+\end_inset
+
+).
+\end_layout
+
+\end_deeper
+\begin_layout Enumerate
+
+\series bold
+Velocity conditions on the boundaries.
+
+\series default
+ Again, for slab subduction this involves inflow conditions on the left
+ boundary and outflow conditions on bottom.
+ See Section
+\begin_inset LatexCommand \ref{sub:Velocity-Boundary-Conditions}
+
+\end_inset
+
+ for details.
+ The other boundaries have no-slip conditions.
+\end_layout
+
+\begin_layout Enumerate
+
+\series bold
+A region where new particles are created, not split from existing particles.
+
+\series default
+ When Gale advects material near an inflowing boundary, this leaves a vacuum.
+ Normally, Gale creates new particles by cloning nearby particles.
+ However, if the cloned particles have already undergone evolution (e.g.,
+ they were strained), then the new particles would no longer be pristine.
+ To fix this, you can specify regions where particles should be created
+ anew by adding something like
+\end_layout
+
+\begin_deeper
+\begin_layout LyX-Code
+
+\family typewriter
+<param name="originalParticleShape">leftBoundaryShape</param>
+\end_layout
+
+\begin_layout Standard
+to the
+\family typewriter
+ReseedSplitting
+\family default
+ struct.
+ An example of this is in the sample input file
+\family typewriter
+subduction.xml
+\family default
+.
+\end_layout
+
+\end_deeper
+\begin_layout Subsection
+Stress Boundary Conditions
+\end_layout
+
+\begin_layout Standard
+If the nature of our problem is that stresses are specified on the boundary
+ rather than velocities, you can specify those conditions using the
+\family typewriter
+StressBC
+\family default
+ component.
+ For example, if you want to simulate an extension model that allows material
+ to well up in the middle, then you would specify a constant stress on the
+ bottom.
+\end_layout
+
+\begin_layout Standard
+StressBC is a component, so it must be inside the list of components (see
+ Section
+\begin_inset LatexCommand \ref{sub:Components}
+
+\end_inset
+
+), not outside the list like the velocity boundary conditions.
+ For example, to specify the stress on the bottom boundary in the
+\begin_inset Formula $y$
+\end_inset
+
+ direction as a constant, add
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="stressBC">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">StressBC</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="ForceVector">mom_force</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Swarm">picIntegrationPoints</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="wall">bottom</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="y_type">double</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="y_value">1.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout Standard
+You can also use the Standard Condition Functions (see Section
+\begin_inset LatexCommand \ref{sec:Standard-Condition-Functions}
+
+\end_inset
+
+), but due to technical issues, you must list Standard Condition Functions
+ before StressBC in the list of components.
+ So, for example, to add a stress condition to the left wall with a Gaussian
+ shape, the complete list of components would be
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="conditionFunctions">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">StgFEM_StandardConditionFunctions</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="stressBCBottom">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">StressBC</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="ForceVector">mom_force</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Swarm">picIntegrationPoints</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="wall">bottom</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="y_type">double</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="y_value">1.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="stressBCLeft">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">StressBC</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="ForceVector">mom_force</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Swarm">picIntegrationPoints</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="wall">left</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="x_type">func</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="x_value">Gaussian</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout Standard
+And then in the list of variables (see Section
+\begin_inset LatexCommand \ref{sub:Variables}
+
+\end_inset
+
+), add the parameters for the
+\family typewriter
+Gaussian
+\family default
+:
+\end_layout
+
+\begin_layout LyX-Code
+<param name="GaussianHeight">1.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+<param name="GaussianWidth">0.1</param>
+\end_layout
+
+\begin_layout LyX-Code
+<param name="GaussianCenter">0.5</param>
+\end_layout
+
+\begin_layout LyX-Code
+<param name="GaussianDim">0</param>
+\end_layout
+
+\begin_layout Section
+Deformed Upper Boundary
+\begin_inset LatexCommand \label{sec:Deformed-Upper-Boundary}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Normally, Gale starts the simulation in a rectangular box.
+ As the simulation proceeds, the boundaries can become distorted, in particular
+ the upper boundary.
+ However, you can also tell Gale to start with an initially deformed upper
+ boundary by adding a
+\family typewriter
+SurfaceAdaptor
+\family default
+ component.
+ A simple example is to make the surface a sinusoid
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="surfaceAdaptor">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">SurfaceAdaptor</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="mesh">mesh-linear</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="sourceGenerator">cartesianGenerator</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="surfaceType">cosine</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <list name="origin">
+\end_layout
+
+\begin_layout LyX-Code
+ <param>0.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+ </list>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="amplitude">0.1</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="frequency">6.28318530718</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+
+\end_layout
+
+\begin_layout Standard
+This sets the height of the surface to
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \[
+h=h_{0}+amplitude*\cos\left(x*frequency\right),\]
+
+\end_inset
+
+ where
+\begin_inset Formula $h_{0}$
+\end_inset
+
+ is the original height.
+\end_layout
+
+\begin_layout Standard
+The other supported functions are
+\family typewriter
+sine
+\family default
+ and
+\family typewriter
+wedge
+\family default
+.
+
+\family typewriter
+sine
+\family default
+ takes the same arguments as the
+\family typewriter
+cosine
+\family default
+ example above.
+
+\family typewriter
+wedge
+\family default
+ takes two arguments,
+\family typewriter
+offset
+\family default
+ and
+\family typewriter
+gradient
+\family default
+, and sets the height to
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \[
+h=\left\{ \begin{array}{cc}
+h_{0} & x<offset\\
+h_{0}+gradient\left(x-offset\right) & x>offset\end{array}\right..\]
+
+\end_inset
+
+ If you want to implement your own surface functions, look in
+\end_layout
+
+\begin_layout LyX-Code
+
+\family typewriter
+src/StGermain/Discretisation/Mesh/src/SurfaceAdaptor.c
+\end_layout
+
+\begin_layout Section
+Standard Condition Functions
+\begin_inset LatexCommand \label{sec:Standard-Condition-Functions}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Standard Condition Functions are functions that you can use to specify initial
+ conditions and boundary conditions.
+ At present, they take in a coordinate
+\begin_inset Formula $(x,y,z)$
+\end_inset
+
+ and output a function
+\begin_inset Formula $f(x,y,z)$
+\end_inset
+
+.
+ They are all defined in the directory
+\family typewriter
+src/StgFEM/plugins/StandardConditionFunctions/
+\family default
+.
+ For the following descriptions, the sides of the box are at
+\begin_inset Formula $x_{min}$
+\end_inset
+
+ and
+\begin_inset Formula $x_{max}$
+\end_inset
+
+, and
+\begin_inset Formula $L\equiv x_{max}-x_{min}$
+\end_inset
+
+, and all names with CamelCase capitalization are variables from the input
+ file.
+\end_layout
+
+\begin_layout Description
+Velocity_SolidBodyRotation Returns the coordinates rotated by
+\family typewriter
+SolidBodyRotationOmega
+\family default
+ around the z axis, centered at the coordinate (
+\family typewriter
+SolidBodyRotationCentreX
+\family default
+,
+\family typewriter
+SolidBodyRotationY
+\family default
+, ), out to a radius
+\family typewriter
+RadiusCylinder
+\family default
+.
+ Specifically, if
+\begin_inset Formula $r<RadiusCylinder$
+\end_inset
+
+
+\begin_inset Formula \[
+\begin{array}{ccc}
+f(x,y,z)_{x} & = & -SolidBodyRotationOmega(y-SolidBodyRotationCentreY)\\
+f(x,y,z)_{y} & = & SolidBodyRotationOmega(x-SolidBodyRotationCentreX)\end{array},\]
+
+\end_inset
+
+ otherwise return 0.
+\end_layout
+
+\begin_layout Description
+Velocity_PartialRotationX Returns the x component of Velocity_SolidBodyRotation.
+\end_layout
+
+\begin_layout Description
+Velocity_PartialRotationY Returns the y component of Velocity_SolidBodyRotation.
+\end_layout
+
+\begin_layout Description
+TaperedRotationX if
+\begin_inset Formula $r<RadiusCylinder$
+\end_inset
+
+, return Velocity_PartialRotationX.
+ If
+\begin_inset Formula $RadiusCylinder<r<TaperedRadius$
+\end_inset
+
+, return
+\begin_inset Formula \[
+VelocityPartialRotationX\left(\frac{TaperedRadius-r}{TaperedRadius-RadiusCylinder}\right).\]
+
+\end_inset
+
+ If
+\begin_inset Formula $r>TaperedRadius$
+\end_inset
+
+, return 0.
+\end_layout
+
+\begin_layout Description
+TaperedRotationY Similar to TaperedRotationX, but returns Velocity_PartialRotati
+onY.
+\end_layout
+
+\begin_layout Description
+Velocity_SimpleShear
+\begin_inset Formula $f(x,y,z)=SimpleShearFactor\left(y-SimpleShearCentreY\right)$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Description
+Velocity_Extension
+\begin_inset Formula $f(x,y,z)=ExtensionFactor\left(x-ExtensionCentreX\right)$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Description
+Velocity_PartialLid_TopLayer Returns 0 if the x coordinate is within one
+ grid point of the boundary; 1 otherwise.
+\end_layout
+
+\begin_layout Description
+Velocity_LinearInterpolationLid
+\begin_inset Formula \[
+f(x,y,z)=bcLeftHandSideValue+\left(\frac{bcRightHandSideValue-bcLeftHandSideValue}{L}\right)x\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Description
+Velocity_Lid_RampWithCentralMax
+\begin_inset Formula $f(x,y,z)=\left\{ \begin{array}{cc}
+2\left(x-x_{min}\right)/L & x<L/2+x_{min}\\
+1-2(x-x_{min}-L/2) & x>L/2+x_{min}\end{array}\right.$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Description
+Velocity_SinusoidalLid
+\begin_inset Formula \[
+f(x,y,z)=\sin\left(\frac{\pi\left(x-x_{min}\right)}{L}sinusoidalLidWavenumber\right)\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Description
+Velocity_Lid_CornerOnly Return 1 if the coordinate is on the right boundary.
+\end_layout
+
+\begin_layout Description
+Temperature_CosineHill Returns a hill defined by a cosine.
+ Specifically, if we define pre-rotated coordinates
+\begin_inset Formula \[
+\begin{array}{ccc}
+x_{pre-rotate} & = & CosineHillCentreX-SolidBodyRotationCentreX\\
+y_{pre-rotate} & = & CosineHillCentreY-SolidBodyRotationCentreY\\
+z_{pre-rotate} & = & CosineHillCentreZ-SolidBodyRotationCentreZ\end{array},\]
+
+\end_inset
+
+ and then rotate them around the z axis by the angle
+\begin_inset Formula $\theta=SolidBodyRotationOmega*t$
+\end_inset
+
+
+\begin_inset Formula \[
+\begin{array}{ccc}
+x_{hill} & = & x_{pre-rotate}\cos\theta-y_{pre-rotate}\sin\theta\\
+y_{hill} & = & x_{pre-rotate}\sin\theta+y_{pre-rotate}\cos\theta\\
+z_{hill} & = & z_{pre-rotate}\end{array},\]
+
+\end_inset
+
+ then
+\begin_inset Formula \[
+f(x,y,z)=\left\{ \begin{array}{cc}
+\frac{CosineHillHeight}{4}\cos\left(\frac{2\pi r}{CosineHillDiameter}\right) & r<CosineHillDiameter\\
+0 & r>CosineHillDiameter\end{array}\right.,\]
+
+\end_inset
+
+ where
+\begin_inset Formula $r$
+\end_inset
+
+ is the distance from the center of the hill
+\begin_inset Formula \[
+r\equiv\sqrt{\left(x-x_{hill}\right)^{2}+\left(y-y_{hill}\right)^{2}+\left(z-z_{hill}\right)^{2}}.\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Description
+LinearWithSinusoidalPerturbation If you scale the
+\begin_inset Formula $y$
+\end_inset
+
+ coordinate
+\begin_inset Formula \[
+y_{scaled}=\left(y-y_{min}\right)/\left(y_{max}-y_{min}\right),\]
+
+\end_inset
+
+ then this returns
+\begin_inset Formula \[
+\begin{array}{ccc}
+f(x,y,z) & = & SinusoidalTempIC\_TopLayerBC\\
+ & & +\left(SinusoidalTempIC\_TopLayerBC-SinusoidalTempIC\_TopLayerBC\right)\left(1-y_{scaled}\right)\\
+ & & +SinusoidalTempIC\_PerturbationAmplitude\\
+ & & *\left(\cos\left(\pi x*SinusoidalTempIC\_HorizontalWaveNumber\right)\right.\\
+ & & +\left.sin\left(\pi ySinusoidalTempIC\_VerticalWaveNumber\right)\right)\end{array}.\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Description
+Temperature_Trigonometry
+\begin_inset Formula \[
+f(x,y,z)=1-\frac{\pi y}{2}\sin\left(\frac{\pi x}{x_{max}-x_{min}}\right).\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Description
+VelicTemperatureIC
+\begin_inset Formula \[
+f(x,y,z)=sigma*\cos\left(\pi wavenumberX\left(\frac{x-x_{min}}{x_{max}-x_{min}}\right)\right)\sin\left(\pi\left(y-y_{min}\right)wavenumberY\right),\]
+
+\end_inset
+
+where the height of the box is constrained to
+\begin_inset Formula $y_{max}-y_{min}=1$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Description
+VelicTemperatureIC_SolB
+\begin_inset Formula \[
+f(x,y,z)=sigma*\cos\left(\pi wavenumberX\left(\frac{x-x_{min}}{x_{max}-x_{min}}\right)\right)\sinh\left(\pi wavenumberY\left(\frac{y-y_{min}}{x-x_{min}}\right)\right),\]
+
+\end_inset
+
+where the height of the box is constrained to
+\begin_inset Formula $y_{max}-y_{min}=1$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Description
+AnalyticalTemperatureIC First, define
+\begin_inset Formula \[
+\begin{array}{ccc}
+x_{0} & \equiv & x-x_{min}\\
+y_{0} & \equiv & y-y_{min}\\
+L & \equiv & x_{max}-x_{min}\\
+H & \equiv & y_{max}-y_{min}\\
+\lambda & \equiv & L/H\end{array},\]
+
+\end_inset
+
+and then compute some intermediate quantities
+\begin_inset Formula \[
+\begin{array}{ccc}
+u_{0} & = & \frac{\lambda^{7/3}}{\left(1+\lambda^{4}\right)^{2/3}}\left(\frac{Ra}{2\sqrt{pi}}\right)^{2/3}\\
+v_{0} & = & u_{0}/\lambda\\
+Q & = & 2\sqrt{\lambda/\left(\pi u_{0}\right)}\\
+T_{u} & = & \frac{1}{2}erf(\left(\frac{1}{2}\left(1-y_{0}\right)\sqrt{u_{0}/x_{0}}\right)\\
+T_{l} & = & 1-\frac{1}{2}erf\left(\frac{1}{2}y_{0}\sqrt{u_{0}/\left(\lambda-x_{0}\right)}\right)\\
+T_{r} & = & \frac{1}{2}+\frac{1}{2}\left(Q/\sqrt{\pi}\right)\sqrt{v_{0}/\left(y_{0}+1\right)}\exp\left(-x_{0}^{2}v_{0}/\left(4y_{0}+4\right)\right)\\
+T_{s} & = & \frac{1}{2}-\frac{1}{2}\left(Q/\sqrt{\pi}\right)\sqrt{v_{0}/\left(2-y_{0}\right)}\exp\left(-\left(\lambda-x_{0}\right)^{2}v_{0}/\left(8-4y_{0}\right)\right)\\
+g & = & T_{u}+T_{l}+T_{r}+T_{s}-1.5\end{array}.\]
+
+\end_inset
+
+ The result then is
+\begin_inset Formula \[
+f(x,y,z)=\left\{ \begin{array}{cc}
+0 & g<0\\
+g & 0<g<1\\
+1 & g>1\end{array}\right..\]
+
+\end_inset
+
+Note that this requires the error function
+\begin_inset Formula $erf$
+\end_inset
+
+ which is not available on all platforms.
+
+\end_layout
+
+\begin_layout Description
+SinusoidalExtension
+\begin_inset Formula \[
+\begin{array}{ccc}
+f(x,y,z) & = & SinusoidalExtensionVelocity+SinusoidalExtensionAmplitude\\
+ & & *\cos\left(2\pi SinusoidalExtensionFrequency\left(t+dt-SinusoidalExtensionPhaseShift\right)\right)\end{array}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Description
+StepFunction This function returns a ramp function in the axis prescribed
+ by the integer
+\begin_inset Formula $StepFunctionDim$
+\end_inset
+
+, where
+\begin_inset Formula $0\Rightarrow x$
+\end_inset
+
+,
+\begin_inset Formula $1\Rightarrow y$
+\end_inset
+
+,
+\begin_inset Formula $2\Rightarrow z$
+\end_inset
+
+.
+ Defining some convenient constants
+\begin_inset Formula \[
+\begin{array}{ccc}
+w & = & coord[dim]\\
+w_{-} & = & StepFunctionLowerOffset\\
+w_{+} & = & StepFunctionUpperOffset\\
+V & = & StepFunctionValue\end{array},\]
+
+\end_inset
+
+then if
+\begin_inset Formula $StepFunctionLessThan$
+\end_inset
+
+ is
+\family typewriter
+True
+\family default
+, then
+\begin_inset Formula \[
+f(x,y,z)=\left\{ \begin{array}{cc}
+0 & w<w_{-}\\
+V\left(\frac{w-w_{-}}{w_{+}-w_{-}}\right) & w_{-}<w<w_{+}\\
+V & w_{+}<w\end{array}\right.,\]
+
+\end_inset
+
+ otherwise it is reversed
+\begin_inset Formula \[
+f(x,y,z)=\left\{ \begin{array}{cc}
+V & w<w_{-}\\
+V\left(\frac{w_{+}-w}{w_{+}-w_{-}}\right) & w_{-}<w<w_{+}\\
+0 & w_{+}<w\end{array}\right.,\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Description
+StepFunctionProduct1 Using a similar scheme as StepFunction to specify the
+ dimension with
+\newline
+
+\begin_inset Formula $StepFunctionProduct1Dim$
+\end_inset
+
+,
+\begin_inset Formula \[
+f(x,y,z)=\left\{ \begin{array}{cc}
+0 & w<StepFunctionProduct1Start\\
+StepFunctionProduct1Value & StepFunctionProduct1Start<w<StepFunctionProduct1End\\
+0 & w>StepFunctionProduct1End\end{array}\right.\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Description
+StepFunctionProduct2
+\end_layout
+
+\begin_layout Description
+StepFunctionProduct3
+\end_layout
+
+\begin_layout Description
+StepFunctionProduct4 These are the same as StepFunctionProduct1 except that
+ they use different variables (e.g.,
+\begin_inset Formula $StepFunctionProduct2Dim$
+\end_inset
+
+ instead of
+\begin_inset Formula $StepFunctionProduct1Dim$
+\end_inset
+
+).
+\end_layout
+
+\begin_layout Description
+Gaussian
+\begin_inset Formula \[
+f(x,y,z)=\left(GaussianHeight\right)\exp\left[-\left(\frac{GaussianCenter-coord[dim]}{GaussianWidth}\right)^{2}\right]\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Verbosity Options
+\end_layout
+
+\begin_layout Standard
+By default, Gale prints out very little when running.
+ To get more information, insert
+\end_layout
+
+\begin_layout LyX-Code
+<param name="journal.info">True</param>
+\end_layout
+
+\begin_layout LyX-Code
+<param name="journal.debug">True</param>
+\end_layout
+
+\begin_layout LyX-Code
+<param name="journal-level.info">2</param>
+\end_layout
+
+\begin_layout LyX-Code
+<param name="journal-level.debug">2</param>
+\end_layout
+
+\begin_layout Standard
+into the variables section (see Section
+\begin_inset LatexCommand \ref{sub:Variables}
+
+\end_inset
+
+).
+ This will print out more information than you need about the components,
+ the solvers, and the number of iterations.
+ In addition, you can get even more information about the solvers from PETSc
+ by appending the
+\begin_inset Quotes sld
+\end_inset
+
+
+\family typewriter
+-ksp_monitor
+\family default
+
+\begin_inset Quotes srd
+\end_inset
+
+ to the command line.
+\end_layout
+
+\begin_layout Chapter
+Output File Format
+\begin_inset LatexCommand \label{cha:Output-File-Format}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Gale outputs four types of files.
+
+\end_layout
+
+\begin_layout Section
+
+\family typewriter
+.dat
+\family default
+ ASCII Files
+\end_layout
+
+\begin_layout Standard
+The first type are ASCII files with
+\family typewriter
+.dat
+\family default
+ extensions.
+ Inside each
+\family typewriter
+.dat
+\family default
+ file are several columns of data.
+ For example,
+\family typewriter
+PressureField.00001.dat
+\family default
+ might have
+\end_layout
+
+\begin_layout LyX-Code
+
+\family typewriter
+0 0.0312539624080715 0.0109361134145122 0 -9.81467103200287
+\end_layout
+
+\begin_layout LyX-Code
+
+\family typewriter
+1 0.0937630718938361 0.0109356986189374 0 17.7373201951569
+\end_layout
+
+\begin_layout LyX-Code
+
+\family typewriter
+2 0.156270066350344 0.0109368543031399 0 -37.0281780188199
+\end_layout
+
+\begin_layout LyX-Code
+
+\family typewriter
+3 0.218780947570009 0.0109343376815161 0 45.6263762140766
+\end_layout
+
+\begin_layout LyX-Code
+
+\family typewriter
+4 0.28128858838265 0.010937987088561 0 -65.2132484518426
+\end_layout
+
+\begin_layout LyX-Code
+...
+\end_layout
+
+\begin_layout Standard
+The first column (0,1,2,3, ...) is the node number, and the second, third,
+ and fourth columns are the x, y, and z coordinates (2D runs still have
+ z data that can be ignored).
+ The last column(s) show the value.
+ The five different types of variables and the order of components is
+\end_layout
+
+\begin_layout Description
+Scalar Value
+\end_layout
+
+\begin_layout Description
+Vector 2D: x y
+\newline
+3D: x, y, z
+\end_layout
+
+\begin_layout Description
+Tensor 2D: xx, xy, yx, yy
+\newline
+3D: xx, xy, xz, yx, yy, yz, zx, zy, zz
+\end_layout
+
+\begin_layout Description
+Symmetric\InsetSpace ~
+Tensor 2D: xx, yy, xy
+\newline
+3D: xx, yy, zz, xy, xz, yz
+\end_layout
+
+\begin_layout Description
+AntiSymmetric\InsetSpace ~
+Tensor 2D: xx, xy, yx, yy
+\newline
+3D: xx, xy, xz, yx, yy, yz, zx, zy,
+ zz (note that xx, yy, and zz are identical to zero)
+\end_layout
+
+\begin_layout Standard
+The complete list of output files per time step with the default components
+ (see Section
+\begin_inset LatexCommand \ref{sec:Basic-Components}
+
+\end_inset
+
+) is
+\end_layout
+
+\begin_layout Description
+Scalar Pressure, StrainRateInvariant, VelocityMagnitude, VelocityGradientsInvari
+ant
+\end_layout
+
+\begin_layout Description
+Vector Velocity
+\end_layout
+
+\begin_layout Description
+Tensor VelocityGradients
+\end_layout
+
+\begin_layout Description
+Symmetric\InsetSpace ~
+Tensor StrainRate
+\end_layout
+
+\begin_layout Description
+Antisymmetric\InsetSpace ~
+Tensor Vorticity
+\end_layout
+
+\begin_layout Standard
+There will also be a timeInfo file, which records the start time and dt
+ for that time step, and materialSwarm which is described in Section
+\begin_inset LatexCommand \ref{sec:.dat-Binary-Files}
+
+\end_inset
+
+.
+ Finally, there will be
+\family typewriter
+.txt
+\family default
+ files from
+\family typewriter
+DumpSwarm
+\family default
+, explained below in Section
+\begin_inset LatexCommand \ref{sec:.txt-Files-(Particle}
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Section
+
+\family typewriter
+.dat
+\family default
+Binary Files (Particle Information)
+\begin_inset LatexCommand \label{sec:.dat-Binary-Files}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+These are the
+\family typewriter
+materialSwarm.*.dat
+\family default
+ files.
+ They are only useful for checkpointing and have a machine dependent format.
+\end_layout
+
+\begin_layout Section
+
+\family typewriter
+.txt
+\family default
+ Files (Particle Information)
+\begin_inset LatexCommand \label{sec:.txt-Files-(Particle}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+These files are output by the
+\family typewriter
+Underworld_DumpSwarm
+\family default
+ plugin.
+ They provide particle information in a more friendly format.
+ The
+\family typewriter
+Underworld_DumpSwarm
+\family default
+ plugin is activated by adding the line
+\end_layout
+
+\begin_layout LyX-Code
+ <param>Underworld_DumpSwarm</param>
+\end_layout
+
+\begin_layout Standard
+to the list of plugins.
+ This line is already in the example input files.
+ The default is to output the ASCII files
+\family typewriter
+yielding.*.txt
+\family default
+.
+ The format of the file is
+\end_layout
+
+\begin_layout LyX-Code
+m x y z
+\family typewriter
+ yielded viscosity
+\end_layout
+
+\begin_layout Standard
+where
+\family typewriter
+m
+\family default
+ is a unique number for the material,
+\family typewriter
+yielded
+\family default
+ is a number between
+\family typewriter
+0
+\family default
+ and
+\family typewriter
+1
+\family default
+ indicating how much a material point has failed, and
+\family typewriter
+viscosity
+\family default
+ is material's isotropic viscosity.
+ If the material does not yield (e.g.
+ is purely viscous), then yielded is always zero.
+
+\end_layout
+
+\begin_layout Standard
+You can also output in csv format for easily reading the data into a spreadsheet
+ like Excel.
+ To do this, just set the variable
+\family typewriter
+outputFormat
+\family default
+ in the global list of variables
+\end_layout
+
+\begin_layout LyX-Code
+<param name="outputFormat">csv</param>
+\end_layout
+
+\begin_layout Standard
+If you want to print out some other property of the material, e.g., non-isotropic
+ viscosity, modify
+\family typewriter
+DumpSwarm
+\family default
+ to provide that information.
+ The source for the plugin is found in the directory
+\end_layout
+
+\begin_layout LyX-Code
+src/Underworld/plugins/Output/DumpSwarm/
+\end_layout
+
+\begin_layout Section
+
+\family typewriter
+.vtk
+\family default
+ Files (Visualization)
+\begin_inset LatexCommand \label{sec:.vtk-Files-(Visualization)}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+These files are output by the
+\family typewriter
+Underworld_VTKOutput
+\family default
+ plugin.
+ These files are in a format understood by a wide variety of visualization
+ programs, sich as
+\begin_inset LatexCommand \htmlurl[ParaView]{paraview.org}
+
+\end_inset
+
+ (recommended),
+\begin_inset LatexCommand \htmlurl[MayaVi]{mayavi.sf.net}
+
+\end_inset
+
+, or
+\begin_inset LatexCommand \htmlurl[Visit]{www.llnl.gov/visit}
+
+\end_inset
+
+.
+ The
+\family typewriter
+Underworld_VTKOutput
+\family default
+ plugin is activated by adding the line
+\end_layout
+
+\begin_layout LyX-Code
+ <param>Underworld_VTKOutput</param>
+\end_layout
+
+\begin_layout Standard
+to the list of plugins.
+ This line is already in the example input files.
+\end_layout
+
+\begin_layout Chapter
+Benchmarks
+\end_layout
+
+\begin_layout Standard
+CIG has worked with Susanne Buiter at NGU to improve the benchmak specifications.
+ Gale has been tested with relaxation of topography, extension, shortening,
+ and subduction models.
+\end_layout
+
+\begin_layout Chapter
+License
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+GNU GENERAL PUBLIC LICENSE Version 2, June 1991.
+ Copyright (C) 1989, 1991 Free Software Foundation, Inc.
+ 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+\series default
+
+\newline
+
+\series medium
+Everyone is permitted to copy and distribute verbatim copies of this license
+ document, but changing it is not allowed.
+\end_layout
+
+\begin_layout Section*
+Preamble
+\end_layout
+
+\begin_layout Standard
+The licenses for most software are designed to take away your freedom to
+ share and change it.
+ By contrast, the GNU General Public License is intended to guarantee your
+ freedom to share and change free software -- to make sure the software
+ is free for all its users.
+ This General Public License applies to most of the Free Software Foundation's
+ software and to any other program whose authors commit to using it.
+ (Some other Free Software Foundation software is covered by the GNU Library
+ General Public License instead.) You can apply it to your programs, too.
+\end_layout
+
+\begin_layout Standard
+When we speak of free software, we are referring to freedom, not price.
+ Our General Public Licenses are designed to make sure that you have the
+ freedom to distribute copies of free software (and charge for this service
+ if you wish), that you receive source code or can get it if you want it,
+ that you can change the software or use pieces of it in new free programs;
+ and that you know you can do these things.
+\end_layout
+
+\begin_layout Standard
+To protect your rights, we need to make restrictions that forbid anyone
+ to deny you these rights or to ask you to surrender the rights.
+ These restrictions translate to certain responsibilities for you if you
+ distribute copies of the software, or if you modify it.
+\end_layout
+
+\begin_layout Standard
+For example, if you distribute copies of such a program, whether gratis
+ or for a fee, you must give the recipients all the rights that you have.
+ You must make sure that they, too, receive or can get the source code.
+ And you must show them these terms so they know their rights.
+\end_layout
+
+\begin_layout Standard
+We protect your rights with two steps:
+\end_layout
+
+\begin_layout Enumerate
+Copyright the software, and
+\end_layout
+
+\begin_layout Enumerate
+Offer you this license which gives you legal permission to copy, distribute
+ and/or modify the software.
+\end_layout
+
+\begin_layout Standard
+Also, for each author's protection and ours, we want to make certain that
+ everyone understands that there is no warranty for this free software.
+ If the software is modified by someone else and passed on, we want its
+ recipients to know that what they have is not the original, so that any
+ problems introduced by others will not reflect on the original authors'
+ reputations.
+\end_layout
+
+\begin_layout Standard
+Finally, any free program is threatened constantly by software patents.
+ We wish to avoid the danger that redistributors of a free program will
+ individually obtain patent licenses, in effect making the program proprietary.
+ To prevent this, we have made it clear that any patent must be licensed
+ for everyone's free use or not licensed at all.
+
+\end_layout
+
+\begin_layout Standard
+The precise terms and conditions for copying, distribution and modification
+ follow.
+\end_layout
+
+\begin_layout Section*
+GNU GENERAL PUBLIC LICENSE TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION
+ AND MODIFICATION
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+begin{itemize}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+item[0.]
+\end_layout
+
+\end_inset
+
+This License applies to any program or other work which contains a notice
+ placed by the copyright holder saying it may be distributed under the terms
+ of this General Public License.
+ The "Program" below refers to any such program or work, and a "work based
+ on the Program" means either the Program or any derivative work under copyright
+ law: that is to say, a work containing the Program or a portion of it,
+ either verbatim or with modifications and/or translated into another language.
+ (Hereinafter, translation is included without limitation in the term "modificat
+ion.") Each licensee is addressed as "you."
+\newline
+
+\newline
+Activities other than copying,
+ distribution and modification are not covered by this License; they are
+ outside its scope.
+ The act of running the Program is not restricted, and the output from the
+ Program is covered only if its contents constitute a work based on the
+ Program (independent of having been made by running the Program).
+ Whether that is true depends on what the Program does.
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+end{itemize}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Enumerate
+You may copy and distribute verbatim copies of the Program's source code
+ as you receive it, in any medium, provided that you conspicuously and appropria
+tely publish on each copy an appropriate copyright notice and disclaimer
+ of warranty; keep intact all the notices that refer to this License and
+ to the absence of any warranty; and give any other recipients of the Program
+ a copy of this License along with the Program.
+
+\end_layout
+
+\begin_deeper
+\begin_layout Standard
+You may charge a fee for the physical act of transferring a copy, and you
+ may at your option offer warranty protection in exchange for a fee.
+
+\end_layout
+
+\end_deeper
+\begin_layout Enumerate
+You may modify your copy or copies of the Program or any portion of it,
+ thus forming a work based on the Program, and copy and distribute such
+ modifications or work under the terms of Section 1 above, provided that
+ you also meet all of these conditions:
+\end_layout
+
+\begin_deeper
+\begin_layout Enumerate
+You must cause the modified files to carry prominent notices stating that
+ you changed the files and the date of any change.
+
+\end_layout
+
+\begin_layout Enumerate
+You must cause any work that you distribute or publish, that in whole or
+ in part contains or is derived from the Program or any part thereof, to
+ be licensed as a whole at no charge to all third parties under the terms
+ of this License.
+
+\end_layout
+
+\begin_layout Enumerate
+If the modified program normally reads commands interactively when run,
+ you must cause it, when started running for such interactive use in the
+ most ordinary way, to print or display an announcement including an appropriate
+ copyright notice and a notice that there is no warranty (or else, saying
+ that you provide a warranty) and that users may redistribute the program
+ under these conditions, and telling the user how to view a copy of this
+ License.
+ (Exception: if the Program itself is interactive but does not normally
+ print such an announcement, your work based on the Program is not required
+ to print an announcement.)
+\end_layout
+
+\begin_layout Standard
+These requirements apply to the modified work as a whole.
+ If identifiable sections of that work are not derived from the Program,
+ and can be reasonably considered independent and separate works in themselves,
+ then this License, and its terms, do not apply to those sections when you
+ distribute them as separate works.
+ But when you distribute the same sections as part of a whole which is a
+ work based on the Program, the distribution of the whole must be on the
+ terms of this License, whose permissions for other licensees extend to
+ the entire whole, and thus to each and every part regardless of who wrote
+ it.
+
+\end_layout
+
+\begin_layout Standard
+Thus, it is not the intent of this section to claim rights or contest your
+ rights to work written entirely by you; rather, the intent is to exercise
+ the right to control the distribution of derivative or collective works
+ based on the Program.
+
+\end_layout
+
+\begin_layout Standard
+In addition, mere aggregation of another work not based on the Program with
+ the Program (or with a work based on the Program) on a volume of a storage
+ or distribution medium does not bring the other work under the scope of
+ this License.
+
+\end_layout
+
+\end_deeper
+\begin_layout Enumerate
+You may copy and distribute the Program (or a work based on it, under Section
+ 2) in object code or executable form under the terms of Sections 1 and
+ 2 above provided that you also do one of the following:
+\end_layout
+
+\begin_deeper
+\begin_layout Enumerate
+Accompany it with the complete corresponding machine-readable source code,
+ which must be distributed under the terms of Sections 1 and 2 above on
+ a medium customarily used for software interchange; or,
+\end_layout
+
+\begin_layout Enumerate
+Accompany it with a written offer, valid for at least three years, to give
+ any third party, for a charge no more than your cost of physically performing
+ source distribution, a complete machine-readable copy of the corresponding
+ source code, to be distributed under the terms of Sections 1 and 2 above
+ on a medium customarily used for software interchange; or,
+\end_layout
+
+\begin_layout Enumerate
+Accompany it with the information you received as to the offer to distribute
+ corresponding source code.
+ (This alternative is allowed only for noncommercial distribution and only
+ if you received the program in object code or executable form with such
+ an offer, in accord with Subsection b above.)
+\end_layout
+
+\begin_layout Standard
+The source code for a work means the preferred form of the work for making
+ modifications to it.
+ For an executable work, complete source code means all the source code
+ for all modules it contains, plus any associated interface definition files,
+ plus the scripts used to control compilation and installation of the executable.
+ However, as a special exception, the source code distributed need not include
+ anything that is normally distributed (in either source or binary form)
+ with the major components (compiler, kernel, and so on) of the operating
+ system on which the executable runs, unless that component itself accompanies
+ the executable.
+\end_layout
+
+\begin_layout Standard
+If distribution of executable or object code is made by offering access
+ to copy from a designated place, then offering equivalent access to copy
+ the source code from the same place counts as distribution of the source
+ code, even though third parties are not compelled to copy the source along
+ with the object code.
+
+\end_layout
+
+\end_deeper
+\begin_layout Enumerate
+You may not copy, modify, sublicense, or distribute the Program except as
+ expressly provided under this License.
+ Any attempt otherwise to copy, modify, sublicense or distribute the Program
+ is void, and will automatically terminate your rights under this License.
+ However, parties who have received copies, or rights, from you under this
+ License will not have their licenses terminated so long as such parties
+ remain in full compliance.
+
+\end_layout
+
+\begin_layout Enumerate
+You are not required to accept this License, since you have not signed it.
+ However, nothing else grants you permission to modify or distribute the
+ Program or its derivative works.
+ These actions are prohibited by law if you do not accept this License.
+ Therefore, by modifying or distributing the Program (or any work based
+ on the Program), you indicate your acceptance of this License to do so,
+ and all its terms and conditions for copying, distributing or modifying
+ the Program or works based on it.
+
+\end_layout
+
+\begin_layout Enumerate
+Each time you redistribute the Program (or any work based on the Program),
+ the recipient automatically receives a license from the original licensor
+ to copy, distribute or modify the Program subject to these terms and conditions.
+ You may not impose any further restrictions on the recipients' exercise
+ of the rights granted herein.
+ You are not responsible for enforcing compliance by third parties to this
+ License.
+
+\end_layout
+
+\begin_layout Enumerate
+If, as a consequence of a court judgment or allegation of patent infringement
+ or for any other reason (not limited to patent issues), conditions are
+ imposed on you (whether by court order, agreement or otherwise) that contradict
+ the conditions of this License, they do not excuse you from the conditions
+ of this License.
+ If you cannot distribute so as to satisfy simultaneously your obligations
+ under this License and any other pertinent obligations, then as a consequence
+ you may not distribute the Program at all.
+ For example, if a patent license would not permit royalty-free redistribution
+ of the Program by all those who receive copies directly or indirectly through
+ you, then the only way you could satisfy both it and this License would
+ be to refrain entirely from distribution of the Program.
+\end_layout
+
+\begin_deeper
+\begin_layout Standard
+If any portion of this section is held invalid or unenforceable under any
+ particular circumstance, the balance of the section is intended to apply
+ and the section as a whole is intended to apply in other circumstances.
+\end_layout
+
+\begin_layout Standard
+It is not the purpose of this section to induce you to infringe any patents
+ or other property right claims or to contest validity of any such claims;
+ this section has the sole purpose of protecting the integrity of the free
+ software distribution system, which is implemented by public license practices.
+ Many people have made generous contributions to the wide range of software
+ distributed through that system in reliance on consistent application of
+ that system; it is up to the author/donor to decide if he or she is willing
+ to distribute software through any other system and a licensee cannot impose
+ that choice.
+
+\end_layout
+
+\begin_layout Standard
+This section is intended to make thoroughly clear what is believed to be
+ a consequence of the rest of this License.
+
+\end_layout
+
+\end_deeper
+\begin_layout Enumerate
+If the distribution and/or use of the Program is restricted in certain countries
+ either by patents or by copyrighted interfaces, the original copyright
+ holder who places the Program under this License may add an explicit geographic
+al distribution limitation excluding those countries, so that distribution
+ is permitted only in or among countries not thus excluded.
+ In such case, this License incorporates the limitation as if written in
+ the body of this License.
+
+\end_layout
+
+\begin_layout Enumerate
+The Free Software Foundation may publish revised and/or new versions of
+ the General Public License from time to time.
+ Such new versions will be similar in spirit to the present version, but
+ may differ in detail to address new problems or concerns.
+
+\end_layout
+
+\begin_deeper
+\begin_layout Standard
+Each version is given a distinguishing version number.
+ If the Program specifies a version number of this License which applies
+ to it and "any later version," you have the option of following the terms
+ and conditions either of that version or of any later version published
+ by the Free Software Foundation.
+ If the Program does not specify a version number of this License, you may
+ choose any version ever published by the Free Software Foundation.
+\end_layout
+
+\end_deeper
+\begin_layout Enumerate
+If you wish to incorporate parts of the Program into other free programs
+ whose distribution conditions are different, write to the author to ask
+ for permission.
+ For software which is copyrighted by the Free Software Foundation, write
+ to the Free Software Foundation; we sometimes make exceptions for this.
+ Our decision will be guided by the two goals of preserving the free status
+ of all derivatives of our free software and of promoting the sharing and
+ reuse of software generally.
+
+\end_layout
+
+\begin_layout Subsection*
+NO WARRANTY
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+begin{itemize}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+item[11.]
+\end_layout
+
+\end_inset
+
+BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY FOR
+ THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW.
+ EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER
+ PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER
+ EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
+ OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
+ THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH
+ YOU.
+ SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY
+ SERVICING, REPAIR OR CORRECTION.
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+item[12.]
+\end_layout
+
+\end_inset
+
+IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL
+ ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR REDISTRIBUTE
+ THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING
+ ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF
+ THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS
+ OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR
+ THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),
+ EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY
+ OF SUCH DAMAGES.
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+end{itemize}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section*
+END OF TERMS AND CONDITIONS
+\end_layout
+
+\begin_layout Subsection*
+How to Apply These Terms to Your New Programs
+\end_layout
+
+\begin_layout Standard
+If you develop a new program, and you want it to be of the greatest possible
+ use to the public, the best way to achieve this is to make it free software
+ which everyone can redistribute and change under these terms.
+
+\end_layout
+
+\begin_layout Standard
+To do so, attach the following notices to the program.
+ It is safest to attach them to the start of each source file to most effectivel
+y convey the exclusion of warranty; and each file should have at least the
+ "copyright" line and a pointer to where the full notice is found.
+ For example:
+\end_layout
+
+\begin_layout Quote
+One line to give the program's name and a brief idea of what it does.
+ Copyright
+\size footnotesize
+© (
+\size default
+year) (name of author)
+\end_layout
+
+\begin_layout Quote
+This program is free software; you can redistribute it and/or modify it
+ under the terms of the GNU General Public License as published by the Free
+ Software Foundation; either version 2 of the License, or (at your option)
+ any later version.
+
+\end_layout
+
+\begin_layout Quote
+This program is distributed in the hope that it will be useful, but WITHOUT
+ ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+ FOR A PARTICULAR PURPOSE.
+ See the GNU General Public License for more details.
+
+\end_layout
+
+\begin_layout Quote
+You should have received a copy of the GNU General Public License along
+ with this program; if not, write to the Free Software Foundation, Inc.,
+ 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+\end_layout
+
+\begin_layout Standard
+Also add information on how to contact you by electronic and paper mail.
+
+\end_layout
+
+\begin_layout Standard
+If the program is interactive, make it output a short notice like this when
+ it starts in an interactive mode:
+\end_layout
+
+\begin_layout Quote
+Gnomovision version 69, Copyright © year name of author Gnomovision comes
+ with ABSOLUTELY NO WARRANTY; for details type `show w'.
+ This is free software, and you are welcome to redistribute it under certain
+ conditions; type `show c' for details.
+
+\end_layout
+
+\begin_layout Standard
+The hypothetical commands `show w' and `show c' should show the appropriate
+ parts of the General Public License.
+ Of course, the commands you use may be called something other than `show
+ w' and `show c'; they could even be mouse-clicks or menu items -- whatever
+ suits your program.
+
+\end_layout
+
+\begin_layout Standard
+You should also get your employer (if you work as a programmer) or your
+ school, if any, to sign a "copyright disclaimer" for the program, if necessary.
+ Here is a sample; alter the names:
+\end_layout
+
+\begin_layout Quote
+Yoyodyne, Inc., hereby disclaims all copyright interest in the program `Gnomovisi
+on' (which makes passes at compilers) written by James Hacker.
+
+\end_layout
+
+\begin_layout Quote
+(signature of Ty Coon)
+\newline
+1 April 1989
+\newline
+Ty Coon, President of Vice
+\end_layout
+
+\begin_layout Standard
+This General Public License does not permit incorporating your program into
+ proprietary programs.
+ If your program is a subroutine library, you may consider it more useful
+ to permit linking proprietary applications with the library.
+ If this is what you want to do, use the GNU Library General Public License
+ instead of this License.
+\end_layout
+
+\begin_layout Bibliography
+
+\bibitem {Fullsack}
+Fullsack, Phillipe (1995).
+ An arbitrary Lagrangian-Eulerian formulation for creeping flows and its
+ application in tectonic models,
+\emph on
+Geophys.
+ J.
+ Int., 120
+\emph default
+, 1-23.
+\end_layout
+
+\begin_layout Bibliography
+
+\bibitem {VPAC}
+Quenette, S., B.
+ Appelbe, M.
+ Gurnis, L.
+ Hodkinson, L.
+ Moresi, and P.
+ Sunter (2005), An Investigation into Design for Performance and Code Maintainab
+ility in High Performance Computing,
+\emph on
+ANZIAM J
+\emph default
+.
+\emph on
+, 46(e),
+\emph default
+ C1001-C1016.
+\end_layout
+
+\begin_layout Bibliography
+
+\bibitem {Underworld}
+Moresi, L.N., F.
+ Dufour, and H.-B.
+ Mühlhaus (2003), A Lagrangian integration point finite element method for
+ large deformation modeling of viscoelastic geomaterials,
+\emph on
+J.
+ Comp.
+ Phys., 184
+\series bold
+,
+\series default
+\emph default
+ 476-497.
+\end_layout
+
+\begin_layout Bibliography
+
+\bibitem {Moresi faulting}
+Moresi, L.N., and H.-B.
+ Mühlhaus (2006), Anisotropic viscous models of large-deformation MohrCoulomb
+ failure,
+\emph on
+Philosophical Magazine, 86,
+\emph default
+ 3287-3305.
+\end_layout
+
+\begin_layout Bibliography
+
+\bibitem {Uzawa}
+ Moresi, L.N., and V.S.
+ Solomatov (1995), Numerical investigation of 2D convection with extremely
+ large viscosity variations,
+\emph on
+Phys.
+ Fluids,
+\emph default
+
+\emph on
+7(9),
+\emph default
+ 2154-2162.
+\end_layout
+
+\begin_layout Bibliography
+
+\bibitem {Ellipsis}
+O'Neill, C., Moresi, L., Müller, D., Albert, R., Dufour, F.
+ (2006), Ellipsis 3D: a particle-in-cell finite element hybrid code for
+ modelling mantle convection and lithospheric deformation,
+\shape italic
+Computers & Geosciences
+\shape default
+,
+\shape italic
+32(10)
+\shape default
+, 1769-1779
+\end_layout
+
+\begin_layout Bibliography
+
+\bibitem {Citcom}
+Zhong, S., M.T.
+ Zuber, L.N.
+ Moresi, and M.
+ Gurnis (2000), The role of temperature-dependent viscosity and surface
+ plates in spherical shell models of mantle convection,
+\shape italic
+J.
+ Geophys.
+ Res.
+\shape default
+,
+\shape italic
+105
+\shape default
+, 11, 063-11, 082
+\end_layout
+
+\end_body
+\end_document
Property changes on: geodyn/3D/MoSST/trunk/doc/mosst.lyx
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Name: svn:executable
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