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[GMRES2stage.git] / paper.tex

diff --git a/paper.tex b/paper.tex
index f60ef9a15f6aea19960f04590472158bcf2ffe65..c8305c5987228cba4786126a629e004165cf7e9a 100644 (file)
--- a/paper.tex
+++ b/paper.tex
@@ -884,13 +884,14 @@ torso3             & 2D/3D problem & 259,156 & 4,429,042 \\
 \label{tab:01}
 \end{center}
 \end{table}
 \label{tab:01}
 \end{center}
 \end{table}

-Chosen parameters  are detailed below.   As by default  the restart of  GMRES is
-performed  every 30  iterations,  we have  chosen  to stop  the  GMRES every  30
-iterations (\emph{i.e.} $max\_iter_{kryl}=30$).  $s$ is set to 8. CGLS is chosen
-to   minimize  the   least-squares  problem   with  the   following  parameters:
+Chosen parameters  are detailed below.   
+We have  stopped  the  GMRES every  30
+iterations (\emph{i.e.}, $max\_iter_{kryl}=30$), which is the default 
+setting of GMRES.  $s$, for its part, has been set to 8. CGLS 
+ minimizes  the   least-squares  problem   with  parameters

 $\epsilon_{ls}=1e-40$ and $max\_iter_{ls}=20$.  The external precision is set to
 $\epsilon_{ls}=1e-40$ and $max\_iter_{ls}=20$.  The external precision is set to

-$\epsilon_{tsirm}=1e-10$.  Those  experiments have been performed  on a Intel(R)
-Core(TM) i7-3630QM CPU @ 2.40GHz with the version 3.5.1 of PETSc.
+$\epsilon_{tsirm}=1e-10$.  These  experiments have been performed  on an Intel(R)
+Core(TM) i7-3630QM CPU @ 2.40GHz with the 3.5.1 version  of PETSc.

 
 
 In  Table~\ref{tab:02}, some  experiments comparing  the solving  of  the linear
 
 
 In  Table~\ref{tab:02}, some  experiments comparing  the solving  of  the linear


@@ -1177,11 +1178,13 @@ experiments up to 16,394 cores have been led to verify that TSIRM runs
 
 
 For  future  work, the  authors'  intention is  to  investigate  other kinds  of
 
 
 For  future  work, the  authors'  intention is  to  investigate  other kinds  of

-matrices, problems, and  inner solvers. The influence of  all parameters must be
+matrices, problems, and  inner solvers. In particular, the possibility 
+to obtain a convergence of TSIRM in situations where the GMRES is divergent will be
+investigated. The influence of  all parameters must be

 tested too, while other methods to minimize the residuals must be regarded.  The
 number of outer  iterations to minimize should become  adaptative to improve the
 overall performances of the proposal.   Finally, this solver will be implemented
 tested too, while other methods to minimize the residuals must be regarded.  The
 number of outer  iterations to minimize should become  adaptative to improve the
 overall performances of the proposal.   Finally, this solver will be implemented

-inside PETSc. This  would be very interesting because it would  allow us to test
+inside PETSc, which would be of interest as it would  allow us to test

 all the non-linear  examples and compare our algorithm  with the other algorithm
 implemented in PETSc.
 
 all the non-linear  examples and compare our algorithm  with the other algorithm
 implemented in PETSc.