From 7122f8d886bcd6191b7eee5017e8c96944ab7e56 Mon Sep 17 00:00:00 2001
From: couturie <raphael.couturier@univ-fcomte.Fr>
Date: Tue, 22 Sep 2015 14:12:20 +0200
Subject: [PATCH] update
---
IJHPCN/biblio.bib | 19 +++++++++++++++++++
IJHPCN/paper.tex | 18 +++++++++++++++---
2 files changed, 34 insertions(+), 3 deletions(-)
diff --git a/IJHPCN/biblio.bib b/IJHPCN/biblio.bib
index 6bb0a3a..0b3b1ec 100644
--- 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 410b7ad..db5f791 100644
--- a/IJHPCN/paper.tex
+++ b/IJHPCN/paper.tex
@@ -911,8 +911,20 @@ taken into account with TSIRM.
%%NEW
+It is well-known that preconditioners have a very strong influence on the
+convergence of linear systems. Previously, we have used some classical
+preconditioners provided by PETSc. HYPRE~\cite{Falgout06} is a very efficient
+preconditioner based on structured multigrid and element-based algebraic
+multigrid algorithms. In Table~\ref{tab:06} we report an experiment that show it
+reduces drastivally the number of iterations but sometimes it is very
+time-consuming compared to other simpler precondititioners. In this table, we
+can see that for $512$ and $2,048$ cores, HYPRE reduces drastically the number
+of iterations for FGMRES to reach the convergence. However, it is very
+time-consuming compared to TSIRM and FGMRES with the ASM preconditioner. For
+$4,096$ and $8,192$ cores, FGMRES with HYPRE did not converge in less than 1000s
+where FGMRES and TSIRM with the ASM converge very quickly. Finally, it can be
+noticed that TSIRM is also faster than FGMRES and it requires less iterations.
-{\bf example ex45/ksp à décrire et commenter en montrant que hypre est pourri avec cet exemple}
\begin{table*}[htbp]
\begin{center}
@@ -925,7 +937,7 @@ taken into account with TSIRM.
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 & -- \\
+ 8192 & 44.35 & 3,197 & 7.6 & 1,083 & 5.84 & >1000 & -- \\
\hline
@@ -982,7 +994,7 @@ caption of the table.
\end{center}
\end{table*}
-In Table~\cite{tab:08}, the results of the experiments with the example ex20 are
+In Table~\ref{tab:08}, the results of the experiments with the example ex20 are
reported. The block Jacobi preconditioner has also been used and CGLS to solve
the minimization step for TSIRM. For this example, we can observ that the number
of iterations for FMGRES increase drastically when the number of cores
--
2.39.5