[cig-commits] commit: Small fixes

[Mercurial]

changeset:   79:571296eee6c2
tag:         tip
user:        Matthew G Knepley <knepley at gmail.com>
date:        Fri Oct 21 10:10:49 2011 -0500
files:       faultRup.tex
description:
Small fixes


diff -r 5b1a88528e53 -r 571296eee6c2 faultRup.tex
--- a/faultRup.tex	Mon Oct 10 18:48:21 2011 -0700
+++ b/faultRup.tex	Fri Oct 21 10:10:49 2011 -0500
@@ -601,7 +601,7 @@ PyLith includes several commonly used fa
 PyLith includes several commonly used fault constitutive models, all
 of which specify the shear traction on the fault $T_f$ as a function
 of the cohesive stress $T_c$, coefficient of friction, $\mu_f$, and
-normal traction $T_m$,
+normal traction $T_n$,
 \begin{equation}
   T_f = T_c - \mu_f T_n.
 \end{equation}
@@ -641,7 +641,7 @@ faces along the fault. In order to impos
 faces along the fault. In order to impose a given fault slip, as in
 equation~(\ref{eqn:fault:disp}), we must represent the displacement on
 both sides of the fault for any vertex on the fault. One option is to
-designate ``fault vertices'' which posses twice as many displacement
+designate ``fault vertices'' which possess twice as many displacement
 degrees of freedom \cite{Aagaard:etal:BSSA:2001}. However, this
 requires storing the global variable indices by cell rather than by
 vertex or adding special fault metadata to the vertices, significantly
@@ -732,7 +732,7 @@ result.
 % We could also extend the fault with a set of ``halo faces'' to divide one side from the other
 
 
-\matt{What about the bug we had with fault ends?}
+\matt{What about the bug we had with fault ends? This is only a problem with refinement at fault ends.}
   
 % ------------------------------------------------------------------
 \section{Solver Customization}
@@ -741,10 +741,10 @@ result.
 
 In order to solve the large, sparse systems of linear equations
 arising in quasi-static simulations, we employ preconditioned Krylov
-subspace methods~\cite{Saad03}. The Krylov iteration generates a small
-subspace by repeatedly applying the linear system operator to a vector
-\matt{Need this explained in less technical jargon. Most geoscientists
-  are not familiar with ``subspace'' and ``linear system operator''.}
+subspace methods~\cite{Saad03}. We create a sequence of vectors by
+repeatedly applying the system matrix to the rhs vector, $\{ A^k b\}$,
+and they form a basis for a subspace, termed the Krylov space. We can
+efficiently find an approximate solution in this subspace.
 Since sparse matrix-vector multiplication is very scalable, this is
 the method of choice for parallel simulation. However, for most
 physically relevant problems, the Krylov solver requires a