\relax 
\@writefile{toc}{\author{Lilia Ziane Khodja}{}}
\@writefile{toc}{\author{Rapha\IeC {\"e}l Couturier}{}}
\@writefile{toc}{\author{Jacques Bahi}{}}
\@writefile{loa}{\addvspace {10\p@ }}
\@writefile{toc}{\contentsline {chapter}{\numberline {10}Solving sparse linear systems with GMRES and CG methods on GPU clusters}{215}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{ch12}{{10}{215}}
\@writefile{toc}{\contentsline {section}{\numberline {10.1}Introduction}{215}}
\newlabel{ch12:sec:01}{{10.1}{215}}
\@writefile{toc}{\contentsline {section}{\numberline {10.2}Krylov iterative methods}{216}}
\newlabel{ch12:sec:02}{{10.2}{216}}
\newlabel{ch12:eq:01}{{10.1}{216}}
\newlabel{ch12:eq:02}{{10.2}{216}}
\newlabel{ch12:eq:03}{{10.3}{216}}
\newlabel{ch12:eq:11}{{10.4}{217}}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.2.1}CG method}{217}}
\newlabel{ch12:sec:02.01}{{10.2.1}{217}}
\newlabel{ch12:eq:04}{{10.5}{217}}
\newlabel{ch12:eq:05}{{10.6}{217}}
\newlabel{ch12:eq:06}{{10.7}{217}}
\newlabel{ch12:eq:07}{{10.8}{217}}
\newlabel{ch12:eq:08}{{10.9}{217}}
\newlabel{ch12:eq:09}{{10.10}{217}}
\@writefile{loa}{\contentsline {algocf}{\numberline {9}{\ignorespaces Left-preconditioned CG method\relax }}{218}}
\newlabel{ch12:alg:01}{{9}{218}}
\newlabel{ch12:eq:10}{{10.11}{218}}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.2.2}GMRES method}{219}}
\newlabel{ch12:sec:02.02}{{10.2.2}{219}}
\newlabel{ch12:eq:12}{{10.12}{219}}
\newlabel{ch12:eq:13}{{10.13}{219}}
\newlabel{ch12:eq:14}{{10.14}{219}}
\newlabel{ch12:eq:15}{{10.15}{219}}
\newlabel{ch12:eq:16}{{10.16}{219}}
\newlabel{ch12:eq:17}{{10.17}{219}}
\newlabel{ch12:eq:18}{{10.18}{219}}
\newlabel{ch12:eq:19}{{10.19}{219}}
\@writefile{loa}{\contentsline {algocf}{\numberline {10}{\ignorespaces Left-preconditioned GMRES method with restarts\relax }}{220}}
\newlabel{ch12:alg:02}{{10}{220}}
\@writefile{toc}{\contentsline {section}{\numberline {10.3}Parallel implementation on a GPU cluster}{221}}
\newlabel{ch12:sec:03}{{10.3}{221}}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.3.1}Data partitioning}{221}}
\newlabel{ch12:sec:03.01}{{10.3.1}{221}}
\@writefile{lof}{\contentsline {figure}{\numberline {10.1}{\ignorespaces A data partitioning of the sparse matrix $A$, the solution vector $x$ and the right-hand side $b$ into four portions.\relax }}{222}}
\newlabel{ch12:fig:01}{{10.1}{222}}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.3.2}GPU computing}{222}}
\newlabel{ch12:sec:03.02}{{10.3.2}{222}}
\@writefile{toc}{\contentsline {subsection}{\numberline {10.3.3}Data communications}{223}}
\newlabel{ch12:sec:03.03}{{10.3.3}{223}}
\@writefile{lof}{\contentsline {figure}{\numberline {10.2}{\ignorespaces Data exchanges between \textit  {Node 1} and its neighbors \textit  {Node 0}, \textit  {Node 2} and \textit  {Node 3}.\relax }}{224}}
\newlabel{ch12:fig:02}{{10.2}{224}}
\@writefile{lof}{\contentsline {figure}{\numberline {10.3}{\ignorespaces Columns reordering of a sparse sub-matrix.\relax }}{225}}
\newlabel{ch12:fig:03}{{10.3}{225}}
\@writefile{toc}{\contentsline {section}{\numberline {10.4}Experimental results}{226}}
\newlabel{ch12:sec:04}{{10.4}{226}}
\@writefile{lof}{\contentsline {figure}{\numberline {10.4}{\ignorespaces General scheme of the GPU cluster of tests composed of six machines, each with two GPUs.\relax }}{226}}
\newlabel{ch12:fig:04}{{10.4}{226}}
\@writefile{lof}{\contentsline {figure}{\numberline {10.5}{\ignorespaces Sketches of sparse matrices chosen from the Davis collection.\relax }}{227}}
\newlabel{ch12:fig:05}{{10.5}{227}}
\@writefile{lot}{\contentsline {table}{\numberline {10.1}{\ignorespaces Main characteristics of sparse matrices chosen from the Davis collection.\relax }}{227}}
\newlabel{ch12:tab:01}{{10.1}{227}}
\@writefile{lot}{\contentsline {table}{\numberline {10.2}{\ignorespaces Performances of the parallel CG method on a cluster of 24 CPU cores vs. on a cluster of 12 GPUs.\relax }}{228}}
\newlabel{ch12:tab:02}{{10.2}{228}}
\@writefile{lot}{\contentsline {table}{\numberline {10.3}{\ignorespaces Performances of the parallel GMRES method on a cluster 24 CPU cores vs. on cluster of 12 GPUs.\relax }}{228}}
\newlabel{ch12:tab:03}{{10.3}{228}}
\newlabel{ch12:eq:20}{{10.20}{229}}
\@writefile{lof}{\contentsline {figure}{\numberline {10.6}{\ignorespaces Parallel generation of a large sparse matrix by four computing nodes.\relax }}{230}}
\newlabel{ch12:fig:06}{{10.6}{230}}
\@writefile{lot}{\contentsline {table}{\numberline {10.4}{\ignorespaces Main characteristics of sparse banded matrices generated from those of the Davis collection.\relax }}{230}}
\newlabel{ch12:tab:04}{{10.4}{230}}
\@writefile{lot}{\contentsline {table}{\numberline {10.5}{\ignorespaces Performances of the parallel CG method for solving linear systems associated to sparse banded matrices on a cluster of 24 CPU cores vs. on a cluster of 12 GPUs.\relax }}{231}}
\newlabel{ch12:tab:05}{{10.5}{231}}
\@writefile{toc}{\contentsline {section}{\numberline {10.5}Conclusion}{231}}
\newlabel{ch12:sec:05}{{10.5}{231}}
\@writefile{lot}{\contentsline {table}{\numberline {10.6}{\ignorespaces Performances of the parallel GMRES method for solving linear systems associated to sparse banded matrices on a cluster of 24 CPU cores vs. on a cluster of 12 GPUs.\relax }}{232}}
\newlabel{ch12:tab:06}{{10.6}{232}}
\@writefile{toc}{\contentsline {section}{Bibliography}{232}}
\@setckpt{Chapters/chapter12/ch12}{
\setcounter{page}{234}
\setcounter{equation}{22}
\setcounter{enumi}{4}
\setcounter{enumii}{0}
\setcounter{enumiii}{0}
\setcounter{enumiv}{10}
\setcounter{footnote}{0}
\setcounter{mpfootnote}{0}
\setcounter{part}{5}
\setcounter{chapter}{10}
\setcounter{section}{5}
\setcounter{subsection}{0}
\setcounter{subsubsection}{0}
\setcounter{paragraph}{0}
\setcounter{subparagraph}{0}
\setcounter{figure}{6}
\setcounter{table}{6}
\setcounter{numauthors}{0}
\setcounter{parentequation}{8}
\setcounter{subfigure}{0}
\setcounter{lofdepth}{1}
\setcounter{subtable}{0}
\setcounter{lotdepth}{1}
\setcounter{lstnumber}{50}
\setcounter{ContinuedFloat}{0}
\setcounter{AlgoLine}{29}
\setcounter{algocfline}{10}
\setcounter{algocfproc}{10}
\setcounter{algocf}{10}
\setcounter{nprt@mantissa@digitsbefore}{0}
\setcounter{nprt@mantissa@digitsafter}{0}
\setcounter{nprt@exponent@digitsbefore}{0}
\setcounter{nprt@exponent@digitsafter}{0}
\setcounter{nprt@digitsfirstblock}{0}
\setcounter{nprt@blockcnt}{0}
\setcounter{nprt@cntprint}{0}
\setcounter{proposition}{1}
\setcounter{theorem}{0}
\setcounter{exercise}{0}
\setcounter{example}{0}
\setcounter{definition}{0}
\setcounter{proof}{1}
\setcounter{lstlisting}{0}
}