X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/GMRES2stage.git/blobdiff_plain/c1552aed123e4154c36983b72f5abd7c1578091f..81dc474c4a3dc51b326e64f816210ad947fc75f0:/paper.tex

diff --git a/paper.tex b/paper.tex
index a4c9b26..2583813 100644
--- a/paper.tex
+++ b/paper.tex
@@ -1051,6 +1051,24 @@ core. It can also  be observed that the difference between CGLS  and LSQR is not
 significant. Both can be good but it seems not possible to know in advance which
 one will be the best.
 
+Table~\ref{tab:05} show a strong scaling experiment with the exemple ex54 on the
+Curie  architecture. So  in  this case,  the  number of  unknownws  is fixed  to
+$204,919,225$ and the number of cores ranges from $512$ to $8192$ with the power
+of two.  The  threshold is fixed to $5e-5$ and only  the $mg$ preconditioner has
+been tested. Here  again we can see that TSIRM is  faster that FGMRES. Efficiecy
+of each algorithms is reported. It  can be noticed that FGMRES is more efficient
+than TSIRM except with $8,192$ cores and that its efficiency is greater that one
+whereas the  efficiency of TSIRM is  lower than one. Nevertheless,  the ratio of
+TSIRM  with any  version  of the  least-squares  method is  always faster.  With
+$8,192$ cores when the number of iterations is far more important for FGMRES, we
+can see that it is only slightly more important for TSIRM.
+
+In  Figure~\ref{fig:02}  we report  the  number  of  iterations per  second  for
+experiments  reported in  Table~\ref{tab:05}.  This Figure  highlights that  the
+number of iterations per  seconds is more of less the same  for FGMRES and TSIRM
+with a little advantage for FGMRES. It  can be explained by the fact that, as we
+have previously explained, that the iterations of the least-sqaure steps are not
+taken into account with TSIRM.
 
 \begin{table*}[htbp]
 \begin{center}
@@ -1081,6 +1099,12 @@ one will be the best.
 \label{fig:02}
 \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. 
 %%%*********************************************************
 %%%*********************************************************
 
@@ -1103,13 +1127,14 @@ experiments up to 16,394 cores have been led to verify that TSIRM runs
 5 or  7 times  faster than GMRES.
 
 
-For future work, the authors' intention is to investigate 
-other kinds of matrices, problems, and inner solvers. 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 inside PETSc.
+For  future  work, the  authors'  intention is  to  investigate  other kinds  of
+matrices, problems, and  inner solvers. 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
+inside PETSc. This  would be very interesting because it would  allow us to test
+all the non-linear  examples and compare our algorithm  with the other algorithm
+implemented in PETSc.
 
 
 % conference papers do not normally have an appendix