[cig-commits] commit: More writing

[Mercurial]

changeset:   74:f73dc35a49c1
tag:         tip
user:        Matthew G. Knepley <knepley at gmail.com>
date:        Wed Sep 07 08:39:29 2011 -0500
files:       faultRup.tex references.bib
description:
More writing


diff -r 20748e3ccedf -r f73dc35a49c1 faultRup.tex
--- a/faultRup.tex	Tue Sep 06 13:43:04 2011 -0700
+++ b/faultRup.tex	Wed Sep 07 08:39:29 2011 -0500
@@ -731,8 +731,13 @@ result.
 
 \subsection{Quasi-static Simulations}
 
-\matt{TODO: Add a paragraph on solving linear system using Krylov
-  methods. Define role of preconditioner.}
+In order to solve the large, sparse systems of linear equations arising in quasi-static simulations, we resort to
+preconditioned Krylov subspace methods~\cite{Saad03}. The Krylov iteration generates a small subspace by repeatedly
+applying the linear system operator to a vector. 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
+preconditioner in order to accelerate convergence. While generic preconditioners exist~\cite{Saad03,Smith:etal:1996}, the
+method must often be specialized to the particular problem. Below, we describe a preconditioner specialized to the fault
+interface problem.
 
 The introduction of Lagrange multipliers to implement the fault slip constraints
 produces the saddle-point problem shown in
diff -r 20748e3ccedf -r f73dc35a49c1 references.bib
--- a/references.bib	Tue Sep 06 13:43:04 2011 -0700
+++ b/references.bib	Wed Sep 07 08:39:29 2011 -0500
@@ -617,8 +617,8 @@
   author    = {Smith, B.~F. and Bj{\o}rstad, P. and Gropp, W.~D.},
   title     = {Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations},
   publisher = {Cambridge University Press},
-  year      = {1996}
-  url       = {http://www.mcs.anl.gov/\~{ }bsmith/ddbook.html},
+  year      = {1996},
+  url       = {http://www.mcs.anl.gov/\~{ }bsmith/ddbook.html}
 }
 
 @Article{Liu:etal:2006,
@@ -775,3 +775,13 @@
    Note     = "http://geodynamics.org",
    Year     = 2011,
 }
+
+ at book{Saad03,
+  author    = {Yousef Saad},
+  title     = {Iterative Methods for Sparse Linear Systems},
+  edition   = {2nd},
+  publisher = {SIAM},
+  year      = {2003}
+}
+
+