lejlf

diff --git a/paper.tex b/paper.tex
index c8305c5987228cba4786126a629e004165cf7e9a..e916be8660c17022990811deef853c39c06ff750 100644 (file)
--- a/paper.tex
+++ b/paper.tex
@@ -894,10 +894,10 @@ $\epsilon_{tsirm}=1e-10$.  These  experiments have been performed  on an Intel(R
 Core(TM) i7-3630QM CPU @ 2.40GHz with the 3.5.1 version  of PETSc.
 
 
 Core(TM) i7-3630QM CPU @ 2.40GHz with the 3.5.1 version  of PETSc.
 
 

-In  Table~\ref{tab:02}, some  experiments comparing  the solving  of  the linear
-systems obtained with the previous matrices  with a GMRES variant and with TSIRM
-are given. In the  second column, it can be noticed that  either GMRES or FGMRES
-(Flexible GMRES)~\cite{Saad:1993} is used to solve the linear system.  According
+In  Table~\ref{tab:02}, experiments comparing 
+a GMRES variant with TSIRM in the resolution of linear systems are given. 
+In the  second column, it can be noticed that  either GMRES or FGMRES
+(Flexible GMRES~\cite{Saad:1993}) is used to solve the linear system.  Depending

 to  the matrices,  different preconditioners  are  used.  With  TSIRM, the  same
 solver and the  same preconditionner are used.  This Table  shows that TSIRM can
 drastically reduce  the number of iterations  to reach the  convergence when the
 to  the matrices,  different preconditioners  are  used.  With  TSIRM, the  same
 solver and the  same preconditionner are used.  This Table  shows that TSIRM can
 drastically reduce  the number of iterations  to reach the  convergence when the


@@ -924,7 +924,7 @@ torso3             & fgmres / sor  & 37.70 & 565 & 34.97 & 510 \\
 \hline
 
 \end{tabular}
 \hline
 
 \end{tabular}

-\caption{Comparison of (F)GMRES and TSIRM with (F)GMRES in sequential with some matrices, time is expressed in seconds.}
+\caption{Comparison between sequential standalone (F)GMRES and TSIRM with (F)GMRES (time in seconds).}

 \label{tab:02}
 \end{center}
 \end{table}
 \label{tab:02}
 \end{center}
 \end{table}


@@ -934,10 +934,10 @@ torso3             & fgmres / sor  & 37.70 & 565 & 34.97 & 510 \\
 
 
 In order to perform larger experiments, we have tested some example applications
 
 
 In order to perform larger experiments, we have tested some example applications

-of  PETSc. Those  applications are  available in  the \emph{ksp}  part  which is
+of  PETSc. Those  applications are  available in  the \emph{ksp}  part,  which is

 suited for scalable linear equations solvers:
 \begin{itemize}
 suited for scalable linear equations solvers:
 \begin{itemize}

-\item ex15  is an example  which solves in  parallel an operator using  a finite
+\item ex15  is an example  that solves in  parallel an operator using  a finite

   difference  scheme.   The  diagonal  is  equal to  4  and  4  extra-diagonals
   representing the neighbors in each directions  are equal to -1. This example is
   used  in many  physical phenomena, for  example, heat  and fluid  flow, wave
   difference  scheme.   The  diagonal  is  equal to  4  and  4  extra-diagonals
   representing the neighbors in each directions  are equal to -1. This example is
   used  in many  physical phenomena, for  example, heat  and fluid  flow, wave