X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/GMRES2stage.git/blobdiff_plain/93cf1631938e6deb8446567aa8bab957ce6c0aa5..eacf4c2eeca7315f0a4a7bc9dec99dc6778843d1:/paper.tex

diff --git a/paper.tex b/paper.tex
index b294efc..4d59b93 100644
--- a/paper.tex
+++ b/paper.tex
@@ -931,8 +931,16 @@ by core. The Juqueen architecture is composed  of IBM PowerPC A2 at 1.6 GHz with
 speed network.
 
 
+In  many situations, using  preconditioners is  essential in  order to  find the
+solution of a linear system.  There are many preconditioners available in PETSc.
+For parallel applications all  the preconditioners based on matrix factorization
+are  not  available. In  our  experiments, we  have  tested  different kinds  of
+preconditioners, however  as it is  not the subject  of this paper, we  will not
+present results with many preconditioners. In  practise, we have chosen to use a
+multigrid (mg)  and successive  over-relaxation (sor). For  more details  on the
+preconditioner in PETSc please consult~\cite{petsc-web-page}.
+
 
-{\bf Description of preconditioners}\\
 
 \begin{table*}[htbp]
 \begin{center}
@@ -960,8 +968,7 @@ speed network.
 
 Table~\ref{tab:03} shows  the execution  times and the  number of  iterations of
 example ex15  of PETSc on the  Juqueen architecture. Different  numbers of cores
-are  studied ranging  from  2,048  up-to 16,383.   Two  preconditioners have  been
-tested: {\it mg} and {\it sor}.   For those experiments,  the number  of components  (or unknowns  of the
+are  studied ranging  from  2,048  up-to 16,383 with the two preconditioners {\it mg} and {\it sor}.   For those experiments,  the number  of components  (or unknowns  of the
 problems)  per core  is fixed  to 25,000,  also called  weak  scaling. This
 number can seem relatively small. In fact, for some applications that need a lot
 of  memory, the  number of  components per  processor requires  sometimes  to be
