X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/GMRES2stage.git/blobdiff_plain/448491bcbd3b99bf6aaeed32bae4854925405051..1e098dfc32858d5c40fdc47bec94526503edf207:/IJHPCN/paper.tex

diff --git a/IJHPCN/paper.tex b/IJHPCN/paper.tex
index 21fa922..9c7ff0c 100644
--- a/IJHPCN/paper.tex
+++ b/IJHPCN/paper.tex
@@ -492,7 +492,7 @@ that the proposed TSIRM converges while the GMRES($m$) does not.
 In this section four kinds of experiments have been performed. First, some experiments on real matrices issued from the sparse matrix florida have been achieved out. Second, some experiments in parallel with some linear problems are reported and analyzed. Third, some experiments in parallÃ¨le with som nonlinear problems are illustrated. Finally some parameters of TSIRM are studied in order to understand their influences.
 
 
-\subsection{Real matrices in sequential}
+\subsection{Real matrices}
 %%ENDNEW
 
 
@@ -776,55 +776,6 @@ taken into account with TSIRM.
 \end{figure}
 
 
-Concerning the  experiments some  other remarks are  interesting.
-\begin{itemize}
-\item We have tested other examples  of PETSc/KSP (ex29, ex45, ex49).  For all these
-  examples,  we have also  obtained similar  gains 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 fact, 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 stopped and restarted
-  without decreasing its convergence. That is  why with GMRES we stop it when it
-  is  naturally restarted (\emph{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  which is  stopped and
-  restarted every  16 iterations (for example),  the normal CG will  be far more
-  efficient.   Some  restarted  CG or  CG  variant  versions  exist and  may  be
-  interesting to study in future works.
-\end{itemize}
-%%%*********************************************************
-%%%*********************************************************
-
-
-%%NEW
-
-\subsection{Nonlinear problems in parallel}
-
-\begin{table*}[htbp]
-\begin{center}
-\begin{tabular}{|r|r|r|r|r|r|r|r|} 
-\hline
-
-  nb. cores   & \multicolumn{2}{c|}{FGMRES/ASM} & \multicolumn{2}{c|}{TSIRM CGLS/ASM} & gain& \multicolumn{2}{c|}{FGMRES/HYPRE}   \\ 
-\cline{2-5} \cline{7-8}
-                    & Time  & \# Iter.  & Time  & \# Iter. &        & Time  & \# Iter.   \\\hline \hline
-   512              & 5.54      & 685    & 2.5 &       570 & 2.21   & 128.9 & 9     \\
-   2048             & 14.95     & 1,560  &  4.32 &     746 & 3.48   & 335.7 & 9 \\
-   4096             & 25.13    & 2,369   & 5.61 &   859    & 4.48   & >1000  & -- \\
-   8192             & 44.35   & 3,197   &  7.6  &  1083    &  5.84  & >1000 &  --   \\
-
-\hline
-
-\end{tabular}
-\caption{Comparison of FGMRES  and TSIRM for ex45 of PETSc/KSP with two preconditioner (ASM and HYPRE)  having 25,000 components per core on Curie ($\epsilon_{tsirm}=1e-10$, $max\_iter_{kryl}=30$, $s=12$, $max\_iter_{ls}=15$, $\epsilon_{ls}=1e-40$),  time is expressed in seconds.}
-\label{tab:06}
-\end{center}
-\end{table*}
-
-
 \begin{figure}[htbp]
 \centering
   \includegraphics[width=0.5\textwidth]{nb_iter_sec_ex45_curie}
@@ -833,6 +784,19 @@ Concerning the  experiments some  other remarks are  interesting.
 \end{figure}
 
 
+%%NEW
+
+\subsection{Parallel nonlinear problems}
+
+With  PETSc,  linear  solvers  are  used inside  nonlinear  solvers.   The  SNES
+(Scalable Nonlinear  Equations Solvers) module  in PETSc implements easy  to use
+methods,  like  Newton-type, quasi-Newton  or  full  approximation scheme  (FAS)
+multigrid to solve systems of nonlinears equations.  As the SNES is based on the
+Krylov methods of PETSc, it is interesting to investigate if the TSIRM method is
+also efficient and scalable with non linear problems.
+
+
+
 
 \begin{table*}[htbp]
 \begin{center}
@@ -877,10 +841,39 @@ Concerning the  experiments some  other remarks are  interesting.
 \end{table*}
 
 
-\subsection{Influcence of parameters for TSIRM}
+\subsection{Influence of parameters for TSIRM}
+
+
+
+
+
+\subsection{Experiments conclusions }
+
+{\bf A refaire}
+
+Concerning the  experiments some  other remarks are  interesting.
+\begin{itemize}
+\item We have tested other examples  of PETSc/KSP (ex29, ex45, ex49).  For all these
+  examples,  we have also  obtained similar  gains 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 fact, 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 stopped and restarted
+  without decreasing its convergence. That is  why with GMRES we stop it when it
+  is  naturally restarted (\emph{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  which is  stopped and
+  restarted every  16 iterations (for example),  the normal CG will  be far more
+  efficient.   Some  restarted  CG or  CG  variant  versions  exist and  may  be
+  interesting to study in future works.
+\end{itemize}
 
 %%ENDNEW
 
+
 %%%*********************************************************
 %%%*********************************************************
 \section{Conclusion}
