X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/GMRES2stage.git/blobdiff_plain/c58e487c34213347636db95b9de6e3db660b6c4b..26d38e217c09735a23eb667846b3869559154681:/IJHPCN/paper.tex

diff --git a/IJHPCN/paper.tex b/IJHPCN/paper.tex
index 7b78160..2e4cfb6 100644
--- a/IJHPCN/paper.tex
+++ b/IJHPCN/paper.tex
@@ -49,9 +49,7 @@
 \makeatletter
 \def\theequation{\arabic{equation}}
 
-%\JOURNALNAME{\TEN{\it Int. J. System Control and Information
-%Processing,
-%Vol. \theVOL, No. \theISSUE, \thePUBYEAR\hfill\thepage}}%
+\JOURNALNAME{\TEN{\it International Journal of High Performance Computing and Networking}}
 %
 %\def\BottomCatch{%
 %\vskip -10pt
@@ -73,10 +71,9 @@
 
 \setcounter{page}{1}
 
-\LRH{F. Wang et~al.}
+\LRH{R. Couturier, L. Ziane Khodja and C. Guyeux}
 
-\RRH{Metadata Based Management and Sharing of Distributed Biomedical
-Data}
+\RRH{TSIRM: A Two-Stage Iteration with least-squares Residual Minimization algorithm}
 
 \VOL{x}
 
@@ -86,7 +83,7 @@ Data}
 
 \BottomCatch
 
-\PUBYEAR{2012}
+\PUBYEAR{2015}
 
 \subtitle{}
 
@@ -109,19 +106,25 @@ Data}
 
 
 \begin{abstract}
-In  this article, a  two-stage iterative  algorithm is  proposed to  improve the
+In  this paper,  a  two-stage iterative  algorithm is  proposed  to improve  the
 convergence  of  Krylov  based  iterative  methods,  typically  those  of  GMRES
-variants.  The  principle of  the  proposed approach  is  to  build an  external
-iteration over the  Krylov method, and to frequently  store its current residual
+variants.   The principle  of  the proposed  approach is  to  build an  external
+iteration over the  Krylov method, and to frequently store  its current residual
 (at each GMRES restart for instance).  After a given number of outer iterations,
 a least-squares minimization step is applied on the matrix composed by the saved
-residuals, in order  to compute a better solution and to  make new iterations if
-required.  It  is proven that the  proposal has the  same convergence properties
-than the  inner embedded  method itself.  Experiments  using up to  16,394 cores
-also  show that the  proposed algorithm  runs around  5 or  7 times  faster than
-GMRES.
+residuals, in order to  compute a better solution and to  make new iterations if
+required.  It  is proven that the  proposal has the same  convergence properties
+than the inner  embedded method itself.
+%%NEW
+Several experiments  have been performed
+with  the PETSc  solver  with  linear and  nonlinear  problems.  They show  good
+speedups   compared  to   GMRES  with   up  to   16,394  cores   with  different
+preconditioners.
+%%ENDNEW
 \end{abstract}
 
+
+
 \KEYWORD{Iterative Krylov methods; sparse linear and non linear systems; two stage iteration; least-squares residual minimization; PETSc.}
 
 %\REF{to this paper should be made as follows: Rodr\'{\i}guez
@@ -131,28 +134,11 @@ GMRES.
 %Semantics and Ontologies}, Vol. x, No. x, pp.xxx\textendash xxx.}
 
 \begin{bio}
-Manuel Pedro Rodr\'iguez Bol\'ivar received his PhD in Accounting at
-the University of Granada. He is a Lecturer at the Department of
-Accounting and Finance, University of Granada. His research
-interests include issues related to conceptual frameworks of
-accounting, diffusion of financial information on Internet, Balanced
-Scorecard applications and environmental accounting. He is author of
-a great deal of research studies published at national and
-international journals, conference proceedings as well as book
-chapters, one of which has been edited by Kluwer Academic
-Publishers.\vs{9}
-
-\noindent Bel\'en Sen\'es Garc\'ia received her PhD in Accounting at
-the University of Granada. She is a Lecturer at the Department of
-Accounting and Finance, University of Granada. Her research
-interests are related to cultural, institutional and historic
-accounting and in environmental accounting. She has published
-research papers at national and international journals, conference
-proceedings as well as chapters of books.\vs{8}
-
-\noindent Both authors have published a book about environmental
-accounting edited by the Institute of Accounting and Auditing,
-Ministry of Economic Affairs, in Spain in October 2003.
+RaphaÃ«l Couturier ....
+
+\noindent Lilia Ziane Khodja ...
+
+\noindent Christophe Guyeux ...
 \end{bio}
 
 
@@ -808,16 +794,16 @@ Concerning the  experiments some  other remarks are  interesting.
 %%NEW
 \begin{table*}[htbp]
 \begin{center}
-\begin{tabular}{|r|r|r|r|r|r|r|} 
+\begin{tabular}{|r|r|r|r|r|r|r|r|} 
 \hline
 
-  nb. cores   & \multicolumn{2}{c|}{FGMRES/ASM} & \multicolumn{2}{c|}{TSIRM CGLS/ASM} & \multicolumn{2}{c|}{FGMRES/HYPRE}   \\ 
-\cline{2-7}
-                    & Time  & \# Iter.  & Time  & \# Iter. & Time  & \# Iter.   \\\hline \hline
-   512              & 5.54      & 685    & 2.5 &       570  & 128.9 & 9     \\
-   2048             & 14.95     & 1,560  &  4.32 &     746   & 335.7 & 9 \\
-   4096             & 25.13    & 2,369   & 5.61 &   859  &   >1000  & -- \\
-   8192             & 44.35   & 3,197   &  7.6  &  1083 & >1000 &  --   \\
+  nb. cores   & \multicolumn{2}{c|}{FGMRES/ASM} & \multicolumn{2}{c|}{TSIRM CGLS/ASM} & gain& \multicolumn{2}{c|}{FGMRES/HYPRE}   \\ 
+\cline{2-5} \cline{7-8}
+                    & Time  & \# Iter.  & Time  & \# Iter. &        & Time  & \# Iter.   \\\hline \hline
+   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 &  --   \\
 
 \hline
 
@@ -835,6 +821,51 @@ Concerning the  experiments some  other remarks are  interesting.
 \label{fig:03}
 \end{figure}
 
+
+
+\begin{table*}[htbp]
+\begin{center}
+\begin{tabular}{|r|r|r|r|r|r|} 
+\hline
+
+  nb. cores   & \multicolumn{2}{c|}{FGMRES/BJAC} & \multicolumn{2}{c|}{TSIRM CGLS/BJAC} & gain   \\ 
+\cline{2-5}
+                    & Time         & \# Iter.  & Time   & \# Iter.  &  \\\hline \hline
+   1024              & 667.92      & 48,732    & 81.65  &     5,087 &  8.18 \\
+   2048             & 966.87       & 77,177    &  90.34 &     5,716 &  10.70\\
+   4096             & 1,742.31     & 124,411   &  119.21 &   6,905  & 14.61\\
+   8192             & 2,739.21     & 187,626   &  168.9  &  9,000   & 16.22\\
+
+\hline
+
+\end{tabular}
+\caption{Comparison of FGMRES  and TSIRM for ex20 of PETSc/SNES with a Block Jacobi  preconditioner  having 100,000 components per core on Curie ($\epsilon_{tsirm}=1e-10$, $max\_iter_{kryl}=30$, $s=12$, $max\_iter_{ls}=15$, $\epsilon_{ls}=1e-40$),  time is expressed in seconds.}
+\label{tab:07}
+\end{center}
+\end{table*}
+
+\begin{table*}[htbp]
+\begin{center}
+\begin{tabular}{|r|r|r|r|r|r|} 
+\hline
+
+  nb. cores   & \multicolumn{2}{c|}{FGMRES/BJAC} & \multicolumn{2}{c|}{TSIRM CGLS/BJAC} & gain  \\ 
+\cline{2-5}
+                    & Time         & \# Iter.  & Time   & \# Iter. &  \\\hline \hline
+   1024              & 159.52      & 11,584    &  26.34  &     1,563  &  6.06  \\
+   2048             & 226.24       & 16,459    &  37.23 &     2,248   &  6.08\\
+   4096             & 391.21     & 27,794   &  50.93 &   2,911  &  7.69\\
+   8192             & 543.23     & 37,770   &  79.21  &  4,324  & 6.86 \\
+
+\hline
+
+\end{tabular}
+\caption{Comparison of FGMRES  and TSIRM for ex14 of PETSc/SNES with a Block Jacobi  preconditioner  having 100,000 components per core on Curie ($\epsilon_{tsirm}=1e-10$, $max\_iter_{kryl}=30$, $s=12$, $max\_iter_{ls}=15$, $\epsilon_{ls}=1e-40$),  time is expressed in seconds.}
+\label{tab:08}
+\end{center}
+\end{table*}
+
+
 %%ENDNEW
 
 %%%*********************************************************
