X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/GMRES2stage.git/blobdiff_plain/9fe58147d9a4e7a4182385b4a397fe96695b7862..cce18db44812b9a67dd4d30ca37ea74fd46f16b1:/paper.tex

diff --git a/paper.tex b/paper.tex
index 32e9a3f..cf61a9e 100644
--- a/paper.tex
+++ b/paper.tex
@@ -1106,11 +1106,25 @@ taken into account with TSIRM.
 \end{figure}
 
 
-Concerning the  experiments some  other remarks are  interesting. We  can tested
-other examples  of PETSc  (ex29, ex45,  ex49). For all  these examples,  we also
-obtained  similar  gain between  GMRES  and TSIRM  but  those  examples are  not
-scalable  with many  cores. In  general,  we had  some problems  with more  than
-$4,096$ cores. 
+Concerning the  experiments some  other remarks are  interesting.
+\begin{itemize}
+\item We  can tested other examples of  PETSc (ex29, ex45, ex49).  For all these
+  examples,  we also obtained  similar gain  between GMRES  and TSIRM  but those
+  examples are  not scalable with many  cores. In general, we  had some problems
+  with more than $4,096$ cores.
+\item We have tested many iterative  solvers available in PETSc.  In fast, it is
+  possible to use most of them with TSIRM. From our point of view, the condition
+  to  use  a  solver inside  TSIRM  is  that  the  solver  must have  a  restart
+  feature. More  precisely, the solver must  support to be  stoped and restarted
+  without decrease its  converge. That is why  with GMRES we stop it  when it is
+  naturraly  restarted (i.e.  with  $m$ the  restart parameter).   The Conjugate
+  Gradient (CG) and all its variants do not have ``restarted'' version in PETSc,
+  so they  are not  efficient.  They  will converge with  TSIRM but  not quickly
+  because if  we compare  a normal CG  with a CG  for which  we stop it  each 16
+  iterations  for example,  the  normal CG  will  be for  more efficient.   Some
+  restarted CG  or CG variant versions exist  and may be interested  to study in
+  future works.
+\end{itemize}
 %%%*********************************************************
 %%%*********************************************************
 
