[cig-commits] r4797 - in long/3D/Gale/trunk: . documentation

[walter at geodynamics.org]

Author: walter
Date: 2006-10-11 13:21:04 -0700 (Wed, 11 Oct 2006)
New Revision: 4797

Modified:
   long/3D/Gale/trunk/
   long/3D/Gale/trunk/documentation/gale.lyx
   long/3D/Gale/trunk/documentation/gale.pdf
Log:
 r717 at earth:  boo | 2006-10-11 13:20:37 -0700
 Update the manual



Property changes on: long/3D/Gale/trunk
___________________________________________________________________
Name: svk:merge
   - 3a629746-de10-0410-b17b-fd6ecaaa963e:/cig:716
   + 3a629746-de10-0410-b17b-fd6ecaaa963e:/cig:717

Modified: long/3D/Gale/trunk/documentation/gale.lyx
===================================================================
--- long/3D/Gale/trunk/documentation/gale.lyx	2006-10-11 20:21:02 UTC (rev 4796)
+++ long/3D/Gale/trunk/documentation/gale.lyx	2006-10-11 20:21:04 UTC (rev 4797)
@@ -1,10 +1,10 @@
-#LyX 1.4.1 created this file. For more info see http://www.lyx.org/
+#LyX 1.4.2 created this file. For more info see http://www.lyx.org/
 \lyxformat 245
 \begin_document
 \begin_header
 \textclass book
 \begin_preamble
-\usepackage{hyperref}
+
 \end_preamble
 \language english
 \inputencoding auto
@@ -75,7 +75,7 @@
 \end_layout
 
 \begin_layout Title
-GALE
+Gale
 \end_layout
 
 \begin_layout Author
@@ -84,9 +84,7 @@
 Walter Landry and Luke Hodkinson
 \newline
 Version
- 0.2.0 
-\newline
-(BETA)
+ 1.0.0 
 \end_layout
 
 \begin_layout Date
@@ -132,11 +130,11 @@
 \end_layout
 
 \begin_layout Section
-Who will use GALE?
+Who will use Gale?
 \end_layout
 
 \begin_layout Standard
-The main audience for GALE is research scientists interested in tectonic
+The main audience for Gale is research scientists interested in tectonic
  modeling.
 \end_layout
 
@@ -145,13 +143,13 @@
 \end_layout
 
 \begin_layout Standard
-Computational Infrastructure for Geodynamics (CIG) is making this source
+CIG (Computational Infrastructure for Geodynamics) 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.
+ careers toward the development of Gale.
  It is essential that you recognize these individuals in the normal scientific
  practice by making appropriate acknowledgements.
  
@@ -160,7 +158,7 @@
 \begin_layout Standard
 The code is based on the method described in Moresi, L.
  N., Dufour, F., Mühlhaus, H.-B.
- A Lagrandian integration point finite element method for large deformation
+ A Lagrangian integration point finite element method for large deformation
  modeling of viscoelastic geomaterials.
  
 \emph on
@@ -173,12 +171,13 @@
 184
 \series default
 , 476-497 (2003).
- The developers are Walter Landry of CIG and Luke Hodkinson of the Victorian
- Partnership for Advanced Computing (VPAC), as well as Louis Moresi's group
- at Monash University.
+ 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.
  Gus Correa and Robert Bialas from the Lamont-Doherty Earth Observatory
  provided valuable user testing.
- The GALE team requests that in your oral presentations and in your paper
+ The Gale team requests that in your oral presentations and in your paper
  acknowledgements that you indicate your use of this code, the authors of
  the code, 
 \begin_inset LatexCommand \htmlurl[CIG]{http://www.geodynamics.org/}
@@ -203,9 +202,9 @@
 \end_layout
 
 \begin_layout Standard
-GALE development is supported by a grant from the National Science Foundation
+Gale development is supported by a grant from the National Science Foundation
  to CIG, managed by the Caltech Institute of Technology.
- However, most of the software components below GALE have been developed
+ However, most of the software components below Gale have been developed
  by the Victoria Partnership for Advanced Computing (VPAC) and Monash University.
 \end_layout
 
@@ -214,373 +213,346 @@
 \end_layout
 
 \begin_layout Section
-About GALE
+About Gale
 \end_layout
 
 \begin_layout Standard
-GALE (
-\series bold
-G
-\series default
-eodynamics 
-\series bold
-A
-\series default
-rbitrary 
-\series bold
-L
-\series default
-agrangian 
-\series bold
-E
-\series default
-ulerian) is a code focusing on orogenesis, rifting, and subduction with
- coupling to surface erosion models.
- In collaboration with the Victoria Partnership for Advanced Computing (VPAC),
- the Computational Infrastructure for Geodynamics has developed GALE in
- response to community demand for a parallel implicit tectonic modeling
- code with three-dimensional capability.
+Gale is a parallel, two or three dimensional, implicit finite element code
+ focusing on 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 be 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
-GALE Computational Approach and Governing Equations
+Gale Computational Approach and Governing Equations
 \end_layout
 
+\begin_layout Subsection
+Infrastructure
+\end_layout
+
 \begin_layout Standard
-There are eight basic steps to GALE's computational approach.
- Note that not all of these steps have been implemented yet.
+Gale uses both a regular grid and particles for simulation.
+ The regular grid is used to solve differential equations, and particles
+ are used to record 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 Enumerate
+\begin_layout Subsection
+Basic Equations
+\end_layout
 
-\series bold
-Compute and solve finite element system on Eulerian grid.
+\begin_layout Standard
+We can decompose the stress tensor 
+\begin_inset Formula $\sigma$
+\end_inset
 
-\series default
- 
-\newline
+ into pressure 
+\begin_inset Formula $p$
+\end_inset
 
-\newline
-This sets up a basic finite element method (FEM) setup using StGermain
- and interpolates between an Eulerian and Lagrangian mesh with PiCellerator.
- The Eulerian grid is logically regular, but it can deform to match the
- upper boundary as it changes (see Fig 1).
- We use rheologies from Underworld as a basis for realistic computations.
+ and deviatoric stress 
+\begin_inset Formula $\tau$
+\end_inset
+
  
 \end_layout
 
-\begin_layout Enumerate
+\begin_layout Standard
+\begin_inset Formula \begin{equation}
+\sigma_{ij}=\tau_{ij}-p\delta_{ij},\label{eq:stress}\end{equation}
 
-\series bold
-Apply surface processes to advect topography.
+\end_inset
 
-\series default
- 
-\newline
+where 
+\begin_inset Formula $\delta$
+\end_inset
 
-\newline
-Because surface processes are still an area of research, GALE does not
- provide a complete solution for this process.
- Rather, GALE provides an API to enable users to plug in their own routines
- and a simple example solution (diffusion).
+ is the Kronecker delta.
+ In its simplest form, Gale solves a conservation equation for momentum
 \end_layout
 
-\begin_layout Enumerate
+\begin_layout Standard
+\begin_inset Formula \begin{equation}
+\tau_{ij,j}-p_{,i}=0,\label{eq:simple momentum conservation}\end{equation}
 
-\series bold
-Compute net vertical Eulerian motion of Eulerian boundaries.
+\end_inset
 
-\series default
- 
-\newline
-
-\newline
-The ability to conform the domain of computation to the surface is the
- distinguishing aspect of current codes, such as PLASTI.
- It is also the most difficult to implement.
- It has two components: 
+subject to the continuity equation
 \end_layout
 
-\begin_deeper
-\begin_layout Enumerate
+\begin_layout Standard
+\begin_inset Formula \begin{equation}
+v_{i,i}=0,\label{eq:continuity}\end{equation}
 
-\series bold
-Compute and track the movement of the boundary.
+\end_inset
 
-\series default
- The boundary is defined by the Lagrangian particles, so we have to compute
- contours to find the boundary.
- Once the boundary is known, computing the movement is the subject of later
- steps in the algorithm.
+where 
+\begin_inset Formula $v$
+\end_inset
+
+ is the velocity.
+ We use the convention that repeated indices (e.g.
  
+\begin_inset Formula $v_{i,i}$
+\end_inset
+
+) imply a sum over all dimensions.
+ So in three dimensions
 \end_layout
 
-\begin_layout Enumerate
+\begin_layout Standard
+\begin_inset Formula \begin{equation}
+v_{i,i}\equiv v_{x,x}+v_{y,y}+v_{z,z}.\label{eq:implicit summation}\end{equation}
 
-\series bold
-Perform all of the needed interpolations to scale the boundary.
+\end_inset
 
-\series default
- When moving the Eulerian grid, Gale only computes the movement of the top
- of the grid and scales the rest of the grid linearly.
- 
+
 \end_layout
 
-\end_deeper
-\begin_layout Enumerate
+\begin_layout Standard
+Note that there is no explicit time dependency (yet).
+ Gale simulates creeping flows, so acceleration terms are neglected and
+ material motion evolves through a series of equilibria.
+ If your boundary condition has a time component, then you may infer a time.
+ For example, if your boundaries move inwards at 1 mm/sec, then the solution
+ when the boudaries have moved 5 mm would correspond to 5 seconds.
+\end_layout
 
-\series bold
-Compute vertical flexural/local isostasy.
+\begin_layout Standard
+Sof far, these equations are very simple, taking no account of gravity or
+ temperature.
+ So this is mostly useful when simulating laboratory experiments.
+\end_layout
 
-\series default
+\begin_layout Standard
+To solve eqs.
  
-\newline
+\begin_inset LatexCommand \ref{eq:simple momentum conservation}
 
-\newline
+\end_inset
 
-\series medium
-This part is just calculating the vertical displacement 
-\series default
-\shape italic
-w
-\series medium
-\shape default
- from vertical flexing of the crust due to changes in the weight on the
- crust.
- This is essentially a part of the boundary condition for the bottom of
- the simulation.
- In a 2D code for the problem shown in Fig 1, this requires solving a pair
- of 1D finite element beam problems.
- In the 3D code, this requires solving a 2D finite element beam problem.
- This is not yet implemented.
-\end_layout
+ and 
+\begin_inset LatexCommand \ref{eq:continuity}
 
-\begin_layout Enumerate
+\end_inset
 
-\series bold
-v is corrected to v=v+w.
- 
-\series default
+, we write 
+\begin_inset Formula $\tau$
+\end_inset
 
-\newline
+ in terms of the rate of strain tensor 
+\begin_inset Formula $D$
+\end_inset
 
-\newline
-This is a trivial step.
+
 \end_layout
 
-\begin_layout Enumerate
+\begin_layout Standard
+\begin_inset Formula \begin{equation}
+\tau_{ij}=2\eta D_{ij}\equiv\eta\left(v_{i,j}+v_{j,i}\right),\label{eq:stress strain}\end{equation}
 
-\series bold
-Interpolate v to get motion of Eulerian grid
-\series default
-.
- 
-\end_layout
+\end_inset
 
-\begin_layout Enumerate
+where 
+\begin_inset Formula $\eta$
+\end_inset
 
-\series bold
-Interpolate v on Lagrangian nodes.
-\end_layout
+ is the viscosity.
+ Inserting this into eq.
+ 
+\begin_inset LatexCommand \ref{eq:simple momentum conservation}
 
-\begin_layout Enumerate
+\end_inset
 
-\series bold
-Regrid Lagrangian fields on Eulerian grid.
+ and simplifying with eq.
  
-\series default
+\begin_inset LatexCommand \ref{eq:continuity}
 
-\newline
+\end_inset
 
-\newline
-This is implemented in PiCellerator.
+ gives
 \end_layout
 
-\begin_layout Section
-GALE History
+\begin_layout Standard
+\begin_inset Formula \begin{equation}
+\eta_{,j}\left(v_{i,j}+v_{j,i}\right)+\eta v_{i,jj}-p_{,i}=0.\label{eq:simple elliptic}\end{equation}
+
+\end_inset
+
+This equation and the continuity equation constitute all of the equations
+ for this system.
+ Gale simulates these equations by putting these quantities on a grid.
+ Gale then approximates derivatives of these quantities by using 
 \end_layout
 
 \begin_layout Standard
-GALE arose from discussions at an NSF-sponsored workshop on Tectonic Modeling
- held in Breckenridge, Colorado.
- 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 much use in lithosphere deformation problems such
- as orogenesis, rifting, 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 is at least as useful as SOPALE and MicroFEM
- for addressing these research areas, 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 Formula \begin{equation}
+\begin{array}{ccc}
+\phi_{,x}(x) & \simeq & \frac{\phi(x+\delta x)-\phi(x-\delta x)}{2\delta x}\\
+\phi_{,xx}(x) & \simeq & \frac{\phi(x+\delta x)-2\phi(x)+\phi(x-\delta x)}{\delta x^{2}}\end{array}.\label{eq:derivative}\end{equation}
+
+\end_inset
+
+Using this, we can represent eqs.
  
-\begin_inset LatexCommand \ref{fig:General-subduction-model}
+\begin_inset LatexCommand \ref{eq:simple elliptic}
 
 \end_inset
 
-.
+ and 
+\begin_inset LatexCommand \ref{eq:continuity}
+
+\end_inset
+
+ in matrix form as 
 \end_layout
 
 \begin_layout Standard
-Walter Landry of CIG and Luke Hodkinson of the Victorian Partnership for
- Advanced Computing (VPAC) are the primary developers of GALE.
- Roger Buck, Robert Bialis, and Gus Correa of Columbia University provided
- valuable user testing.
- 
-\begin_inset Float figure
-placement H
-wide false
-sideways false
-status open
+\begin_inset Formula \begin{equation}
+\left(\begin{array}{cc}
+K & G\\
+G^{T}\end{array}\right)\left(\begin{array}{c}
+v\\
+p\end{array}\right)=\left(\begin{array}{c}
+0\\
+0\end{array}\right),\label{eq:matrix form}\end{equation}
 
-\begin_layout Caption
-\begin_inset LatexCommand \label{fig:General-subduction-model}
+\end_inset
 
+where 
+\begin_inset Formula $G$
 \end_inset
 
-General subduction model from Fullsack (1995).
- The basic subduction model can be modified by introducing isostasy and/or
- boundary mass fluxes.
- (a) Flexural or local isostasy.
- Every Eularian 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 $^{\text{+}}$
+ is the simple gradient operator and 
+\begin_inset Formula $K$
 \end_inset
 
- into the domain, due to tectonic convergence; (2) the deposition flux 
-\begin_inset Formula $\text{e}^{+}$
+ is a more complicated submatrix depending on material properties.
+\begin_inset Foot
+status open
+
+\begin_layout Standard
+At this point, it is common in many codes to introduce a penalty function
+ to make the right hand side of the continuity equation 
+\begin_inset LatexCommand \ref{eq:continuity}
+
 \end_inset
 
- onto the domain, due to surface processes; (3) the deposition flux 
-\begin_inset Formula $\text{e}^{-}$
+ non-zero.
+ This would allow us to eliminate 
+\begin_inset Formula $p$
 \end_inset
 
- from the domain, due to surface processes; (4) the crustal subduction flux
- 
-\begin_inset Formula $\text{cs}^{-}$
+ from the equation, leading to a simpler set of equations.
+\end_layout
+
 \end_inset
 
- from the domain, due to the entrainment of crustal material from the subducting
- plate.
- 
+ This implies the separate relations
 \end_layout
 
 \begin_layout Standard
-\noindent
-\begin_inset Graphics
-	filename images/GALE_image1.eps
+\begin_inset Formula \begin{equation}
+\begin{array}{ccc}
+Kv+Gp & = & 0\\
+G^{T}v & = & 0\end{array}.\label{eq:expanded matrix}\end{equation}
 
 \end_inset
 
+We can then eliminate velocity by premultiplying by 
+\begin_inset Formula $G^{T}K^{-1}$
+\end_inset
 
-\end_layout
-
+ and using 
+\begin_inset Formula $G^{T}v=0$
 \end_inset
 
  
 \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}
+\begin_inset Formula \begin{equation}
+G^{T}K^{-1}Gp=0.\label{eq:final simple elliptic}\end{equation}
 
 \end_inset
 
+This equation is solved using the Uzawa algorithm 
+\begin_inset LatexCommand \cite{key-2}
+
+\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 
+Gravity
 \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.
+Gravity is accounted for by adding a body force term to eq.
  
-\begin_inset LatexCommand \htmlurl[StGermain Web Site]{https://csd.vpac.org/twiki/bin/view/Stgermain/WebHome}
+\begin_inset LatexCommand \ref{eq:simple momentum conservation}
 
 \end_inset
 
 
 \end_layout
 
-\begin_layout Subsection
-PETSc
+\begin_layout Standard
+\begin_inset Formula \begin{equation}
+\tau_{ij,j}-p_{,i}=f_{i},\label{eq:body force}\end{equation}
+
+\end_inset
+
+where
 \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]{http://www-unix.mcs.anl.gov/petsc/petsc-as/}
+\begin_inset Formula \begin{equation}
+\begin{array}{ccc}
+f_{x} & = & 0\\
+f_{y} & = & 0\\
+f_{z} & = & -g\rho\end{array}.\label{eq:gravity body force}\end{equation}
 
 \end_inset
 
+ This modifies eq.
+ 
+\begin_inset LatexCommand \ref{eq:matrix form}
 
-\end_layout
+\end_inset
 
-\begin_layout Subsection
-StgFEM 
+ to 
 \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]{https://csd.vpac.org/twiki/bin/view/Stgfem/WebHome}
+\begin_inset Formula \begin{equation}
+\left(\begin{array}{cc}
+K & G\\
+G^{T}\end{array}\right)\left(\begin{array}{c}
+v\\
+p\end{array}\right)=\left(\begin{array}{c}
+f\\
+0\end{array}\right).\label{eq:matrix form}\end{equation}
 
 \end_inset
 
@@ -588,49 +560,82 @@
 \end_layout
 
 \begin_layout Subsection
-PiCellerator 
+Temperature
 \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.
+Temperature is included by solving the energy equation
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \begin{equation}
+\frac{dT}{dt}=\kappa\nabla^{2}T+Q,\label{eq:energy}\end{equation}
+
+\end_inset
+
+ where 
+\begin_inset Formula $d/dt$
+\end_inset
+
+ is the material time derivative (taken at a point moving with respect to
+ the fluid), 
+\begin_inset Formula $T$
+\end_inset
+
+ is the temperature, 
+\begin_inset Formula $\kappa$
+\end_inset
+
+ is the thermal diffusivity, and 
+\begin_inset Formula $Q$
+\end_inset
+
+ is the rate of energy production (e.g.
+ from radiogenic sources).
+ Note that eq.
  
-\begin_inset LatexCommand \htmlurl[PICellerator Web Site]{https://csd.vpac.org/twiki/bin/view/PICellerator/WebHome}
+\begin_inset LatexCommand \ref{eq:energy}
 
 \end_inset
 
-
+ introduces time into the equation.
 \end_layout
 
-\begin_layout Subsection
-UnderWorld 
+\begin_layout Section
+Gale History
 \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 (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).
+Gale arose from discussions at an NSF-sponsored workshop on Tectonic Modeling
+ held in Breckenridge, Colorado.
+ 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 much use in lithosphere deformation problems such
+ as orogenesis, rifting, 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 is at least as useful as SOPALE and MicroFEM
+ for addressing these research areas, 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 \htmlurl[UnderWorld Web Site]{http://wasabi.maths.monash.edu.au/twiki/view/Software/Underworld}
+\begin_inset LatexCommand \ref{fig:General-subduction-model}
 
 \end_inset
 
-
+.
 \end_layout
 
 \begin_layout Standard
+Walter Landry of CIG and Luke Hodkinson of the Victorian Partnership for
+ Advanced Computing (VPAC) are the primary developers of Gale.
+ Roger Buck, Robert Bialis, and Gus Correa of Columbia University provided
+ valuable user testing.
+ 
 \begin_inset Float figure
 placement H
 wide false
@@ -638,18 +643,50 @@
 status open
 
 \begin_layout Caption
-\begin_inset LatexCommand \label{fig:Mapping-between-MicroFEM}
+\begin_inset LatexCommand \label{fig:General-subduction-model}
 
 \end_inset
 
-Mapping between MicroFEM and GALE 
-\newline
+General subduction model from Fullsack (1995).
+ The basic subduction model can be modified by introducing isostasy and/or
+ boundary mass fluxes.
+ (a) Flexural or local isostasy.
+ Every Eularian 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
 \begin_inset Graphics
-	filename images/GALE_imag.eps
+	filename images/GALE_image1.eps
 
 \end_inset
 
@@ -658,7 +695,7 @@
 
 \end_inset
 
-
+ 
 \end_layout
 
 \begin_layout Chapter
@@ -689,7 +726,7 @@
 \end_layout
 
 \begin_layout Standard
-GALE can be downloaded from the 
+Gale can be downloaded from the 
 \begin_inset LatexCommand \htmlurl[CIG Website]{http://www.geodynamics.org/cig/software/packages/gale/}
 
 \end_inset
@@ -775,11 +812,11 @@
 \end_layout
 
 \begin_layout Chapter
-Running GALE
+Running Gale
 \end_layout
 
 \begin_layout Section
-GALE Usage
+Gale Usage
 \end_layout
 
 \begin_layout Standard
@@ -790,7 +827,7 @@
 \end_layout
 
 \begin_layout LyX-Code
-ln -s /home/walter/gale-bin/bin/Underworld
+ln -s /home/walter/Gale-bin/bin/Underworld
 \end_layout
 
 \begin_layout Subsection
@@ -998,7 +1035,7 @@
 \end_layout
 
 \begin_layout Chapter
-Modifying GALE
+Modifying Gale
 \end_layout
 
 \begin_layout Section
@@ -1014,11 +1051,178 @@
 \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]{https://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]{http://www-unix.mcs.anl.gov/petsc/petsc-as/}
+
+\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]{https://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]{https://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 (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]{http://wasabi.maths.monash.edu.au/twiki/view/Software/Underworld}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\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 
+\newline
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Graphics
+	filename images/GALE_imag.eps
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
 System Decription
 \end_layout
 
 \begin_layout Standard
-GALE, like StG_FEM, formulates implicit finite element systems, with the
+Gale uses StG_FEM 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.
@@ -1235,8 +1439,8 @@
 0D and 1D Shear Tests
 \end_layout
 
-\begin_layout Chapter
-References
+\begin_layout Standard
+
 \end_layout
 
 \begin_layout Chapter
@@ -1831,8 +2035,12 @@
 
 \end_layout
 
-\begin_layout Chapter
-How to Apply These Terms to Your New Programs
+\begin_layout Standard
+\align center
+
+\shape smallcaps
+\size large
+How to Apply These Ters to Your New Programs
 \end_layout
 
 \begin_layout Standard
@@ -1987,5 +2195,19 @@
 , 476-497 (2003).
 \end_layout
 
+\begin_layout Bibliography
+
+\bibitem {key-2}
+ Moresi, L.
+ N., Solomatov, V.
+ S., Numerical investigation of 2D convection with extremely large viscosity
+ variations, Phys.
+ Fluids 
+\series bold
+7
+\series default
+ (9), 2154-2162 (1995).
+\end_layout
+
 \end_body
 \end_document

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