[cig-commits] r16901 - in short/3D/PyLith/trunk/doc/userguide: boundaryconditions install
brad at geodynamics.org
brad at geodynamics.org
Fri Jun 4 17:57:40 PDT 2010
Author: brad
Date: 2010-06-04 17:57:40 -0700 (Fri, 04 Jun 2010)
New Revision: 16901
Modified:
short/3D/PyLith/trunk/doc/userguide/boundaryconditions/boundaryconditions.lyx
short/3D/PyLith/trunk/doc/userguide/install/install.lyx
Log:
Revised some notation. Minor edits.
Modified: short/3D/PyLith/trunk/doc/userguide/boundaryconditions/boundaryconditions.lyx
===================================================================
--- short/3D/PyLith/trunk/doc/userguide/boundaryconditions/boundaryconditions.lyx 2010-06-04 22:14:09 UTC (rev 16900)
+++ short/3D/PyLith/trunk/doc/userguide/boundaryconditions/boundaryconditions.lyx 2010-06-05 00:57:40 UTC (rev 16901)
@@ -2330,8 +2330,12 @@
\begin_inset Formula $\underline{C}$
\end_inset
- is a matrix of direction cosines relating the relative motion across the
- fault to the vector of fault slip,
+ is composed of rotation submatrices,
+\begin_inset Formula $\underline{R}$
+\end_inset
+
+, associated with the direction cosines relating the relative displacements
+ across the fault to the vector of fault slip,
\begin_inset Formula $\overrightarrow{d}$
\end_inset
@@ -2364,7 +2368,7 @@
\end_inset
denotes a conventional degree of freedom and
-\begin_inset Formula $p$
+\begin_inset Formula $k$
\end_inset
denotes a degree of freedom associated with a Lagrange multiplier.
@@ -4332,13 +4336,13 @@
time step) and the value computed from the fault constitutive model.
Starting from our system of algebraic equations,
\begin_inset Formula \begin{equation}
-A_{ij}^{nm}u_{j}^{m}+C_{ji}^{pn}l_{j}=b_{i}^{n},\end{equation}
+A_{ij}^{nm}u_{j}^{m}+C_{ji}^{pn}l_{j}^{p}=b_{i}^{n},\end{equation}
\end_inset
we compute the sensitivity for the given loading and boundary conditions,
\begin_inset Formula \begin{equation}
-A_{ij}^{nm}\partial u_{j}^{m}=-C_{ji}^{pn}\partial l_{j}.\end{equation}
+A_{ij}^{nm}\partial u_{j}^{m}=-C_{ji}^{pn}\partial l_{j}^{p}.\end{equation}
\end_inset
@@ -4359,8 +4363,8 @@
\begin_inset Formula \begin{equation}
A=\left(\begin{array}{ccc}
A_{0} & A_{1} & A_{2}\\
-A_{3} & A^{-} & 0\\
-A_{4} & 0 & A^{+}\end{array}\right),\end{equation}
+A_{3} & A_{n-} & 0\\
+A_{4} & 0 & A_{n+}\end{array}\right),\end{equation}
\end_inset
@@ -4369,21 +4373,36 @@
associated with vertices on either the positive or negative sides of the
fault,
\begin_inset Formula \begin{gather}
-A_{ij}^{nm-}\partial u_{j}^{m}=-C_{ij}^{pn}\partial l_{j},\\
-A_{ij}^{nm+}\partial u_{j}^{m}=C_{ij}^{pn}\partial l_{j},\end{gather}
+A_{ij}^{nm-}\partial u_{j}^{m-}=-R_{ij}^{pn}\partial l_{j}^{p},\\
+A_{ij}^{nm+}\partial u_{j}^{m+}=R_{ij}^{pn}\partial l_{j}^{p},\end{gather}
\end_inset
-where we have explicitly differentiated between the signs of the terms in
-
-\begin_inset Formula $C$
+where we have replace
+\begin_inset Formula $\underline{C}$
\end_inset
- for the positive and negative sides of the fault.
+ with
+\begin_inset Formula $\underline{R}$
+\end_inset
+
+ to denote the explicit inclusion of the signs for the terms in
+\begin_inset Formula $\underline{C}$
+\end_inset
+
+ associated with the positive (
+\begin_inset Formula $n^{+}$
+\end_inset
+
+) and negative (
+\begin_inset Formula $n^{-}$
+\end_inset
+
+) sides of the fault.
After solving these two linear systems of equations, we compute the increment
in slip using
\begin_inset Formula \begin{equation}
-\partial d_{i}^{p}=C_{ij}^{pn}\partial u_{j}^{n}.\end{equation}
+\partial d_{i}^{p}=R_{ij}^{pn}(\partial u_{j}^{n+}-\partial u_{j}^{n+}).\end{equation}
\end_inset
@@ -4411,10 +4430,14 @@
\end_inset
By not allowing the fault interface to overlap with the absorbing boundary,
- the terms in A for a given vertex are identical and the expression on the
- right-hand side reduces to
+ the terms in
+\begin_inset Formula $A$
+\end_inset
+
+ for a given vertex are identical and the expression on the right-hand side
+ reduces to
\begin_inset Formula \begin{equation}
-\partial d_{i}^{p}=-\left(\frac{1}{A^{+}}+\frac{1}{A^{-}}\right)\partial l_{i}^{p}.\end{equation}
+\partial d_{i}^{p}=-\left(\frac{1}{A^{n+}}+\frac{1}{A^{n-}}\right)\partial l_{i}^{p}.\end{equation}
\end_inset
Modified: short/3D/PyLith/trunk/doc/userguide/install/install.lyx
===================================================================
--- short/3D/PyLith/trunk/doc/userguide/install/install.lyx 2010-06-04 22:14:09 UTC (rev 16900)
+++ short/3D/PyLith/trunk/doc/userguide/install/install.lyx 2010-06-05 00:57:40 UTC (rev 16901)
@@ -800,24 +800,22 @@
\end_inset
).
- We strongly recommend downloading the latest PyLith and PETSc source code
- directly from the source code repositories, instead of using the source
- packages; see Section
+ Downloading the latest PyLith and PETSc source code directly from the source
+ code repositories, instead of using the source packages (see Section
\begin_inset CommandInset ref
LatexCommand ref
reference "sec:Software-Repository"
\end_inset
- later in this chapter.
- Note that this requires additional tools; see Section
+ later in this chapter) requires additional tools (see Section
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Additional-Tools"
\end_inset
-.
+).
\end_layout
\begin_layout Subsection
@@ -950,8 +948,7 @@
\begin_layout LyX-Code
\size small
-http://geodynamics.org/cig/software/packages/short/pylith/petsc-dev-pylith-1_1_0.t
-gz
+http://geodynamics.org/cig/software/packages/short/pylith/petsc-dev-pylith-1.5.0.tgz
\end_layout
\begin_layout Standard
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