X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/Krylov_multi.git/blobdiff_plain/8dec794b01b4893a1ccc93250b6108a852feb2f7..1aae0aa7fe4cab80db08382a65985baef5853fb1:/krylov_multi.tex?ds=sidebyside

diff --git a/krylov_multi.tex b/krylov_multi.tex
index 61c1e28..3482e92 100644
--- a/krylov_multi.tex
+++ b/krylov_multi.tex
@@ -29,7 +29,7 @@
 
 
 \begin{abstract}
-In  this  paper we  revist  the  krylov  multisplitting algorithm  presented  in
+In  this paper  we  revisit  the krylov  multisplitting  algorithm presented  in
 \cite{huang1993krylov}  which  uses  a  scalar  method to  minimize  the  krylov
 iterations computed by a multisplitting algorithm. Our new algorithm is based on
 a  parallel multisplitting  algorithm  with few  blocks  of large  size using  a
@@ -328,6 +328,31 @@ synchronizations   by   using   the   MPI   collective   communication
 subroutines.
 
 
+\section{Experiments}
+
+In order  to illustrate  the interest  of our algorithm.   We have  compared our
+algorithm  with  the  GMRES  method  which  a very  well  used  method  in  many
+situations.  We have chosen to focus on only one problem which is very simple to
+implement: a 3 dimension Poisson problem.
+
+\begin{equation}
+\left\{
+                \begin{array}{ll}
+                  \nabla u&=f \mbox{~in~} \omega\\
+                  u &=0 \mbox{~on~}  \Gamma=\partial \omega
+                \end{array}
+              \right.
+\end{equation}
+
+After discretization, with a finite  difference scheme, a seven point stencil is
+obtained.
+
+\section{Conclusion and perspectives}
+
+Other applications (=> other matrices)\\
+Larger experiments\\
+Async\\
+Overlapping
 
 
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