update

diff --git a/IJHPCN/biblio.bib b/IJHPCN/biblio.bib
index 6bb0a3aa5875117e7ed5d20270806d555ba15af0..0b3b1ec1c9ae88bb4ab5223525f93b796007e8a3 100644 (file)
--- a/IJHPCN/biblio.bib
+++ b/IJHPCN/biblio.bib
@@ -247,3 +247,22 @@ publisher = {Springer},
 year = 2015,
 
 }
+
+
+@InCollection{Falgout06,
+  author =     "Robert D. Falgout and Jim E. Jones and Ulrike Meier
+                Yang",
+  editor =     "Are Magnus Bruaset and Aslak Tveito",
+  title =      "The Design and Implementation of hypre, a Library of
+                Parallel High Performance Preconditioners",
+  booktitle =  "Numerical Solution of Partial Differential Equations
+                on Parallel Computers",
+  series =     "Lecture Notes in Computational Science and
+                Engineering",
+  pages =      "267--294",
+  publisher =  "Springer-Verlag",
+  address =    "New York",
+  year =       "2006",
+  keywords =   "parallel software tools,",
+  note =       "ch 8,",
+}
\ No newline at end of file

diff --git a/IJHPCN/paper.tex b/IJHPCN/paper.tex
index 410b7ad1f251f96186c1c5f95fe69bebd769f214..db5f79102f8bbe5d0f48aac4cb900ac65a3a0483 100644 (file)
--- a/IJHPCN/paper.tex
+++ b/IJHPCN/paper.tex
@@ -911,8 +911,20 @@ taken into account with TSIRM.
 \r
 \r
 %%NEW\r
+It  is well-known  that  preconditioners have  a very  strong  influence on  the\r
+convergence  of  linear  systems.   Previously,  we  have  used  some  classical\r
+preconditioners provided  by PETSc.  HYPRE~\cite{Falgout06} is  a very efficient\r
+preconditioner  based  on  structured   multigrid  and  element-based  algebraic\r
+multigrid algorithms. In Table~\ref{tab:06} we report an experiment that show it\r
+reduces  drastivally  the  number  of   iterations  but  sometimes  it  is  very\r
+time-consuming compared  to other simpler  precondititioners. In this  table, we\r
+can see that  for $512$ and $2,048$ cores, HYPRE  reduces drastically the number\r
+of  iterations  for FGMRES  to  reach  the  convergence.   However, it  is  very\r
+time-consuming compared  to TSIRM  and FGMRES with  the ASM  preconditioner. For\r
+$4,096$ and $8,192$ cores, FGMRES with HYPRE did not converge in less than 1000s\r
+where FGMRES and  TSIRM with the ASM  converge very quickly. Finally,  it can be\r
+noticed that TSIRM is also faster than FGMRES and it requires less iterations.\r
 \r
-{\bf example ex45/ksp à décrire et commenter en montrant que hypre est pourri avec cet exemple}\r
 \r
 \begin{table*}[htbp]\r
 \begin{center}\r
@@ -925,7 +937,7 @@ taken into account with TSIRM.
    512              & 5.54      & 685    & 2.5 &       570 & 2.21   & 128.9 & 9     \\\r
    2048             & 14.95     & 1,560  &  4.32 &     746 & 3.48   & 335.7 & 9 \\\r
    4096             & 25.13    & 2,369   & 5.61 &   859    & 4.48   & >1000  & -- \\\r
-   8192             & 44.35   & 3,197   &  7.6  &  1083    &  5.84  & >1000 &  --   \\\r
+   8192             & 44.35   & 3,197   &  7.6  &  1,083    &  5.84  & >1000 &  --   \\\r
 \r
 \hline\r
 \r
@@ -982,7 +994,7 @@ caption of the table.
 \end{center}\r
 \end{table*}\r
 \r
-In Table~\cite{tab:08}, the results of the experiments with the example ex20 are\r
+In Table~\ref{tab:08}, the results of the experiments with the example ex20 are\r
 reported. The block  Jacobi preconditioner has also been used  and CGLS to solve\r
 the minimization step for TSIRM. For this example, we can observ that the number\r
 of  iterations  for  FMGRES  increase  drastically  when  the  number  of  cores\r