BookGPU/Chapters/chapter12/ch12.aux

   1 \relax
   2 \@writefile{toc}{\author{Lilia Ziane Khodja}{}}
   3 \@writefile{toc}{\author{Rapha\IeC {\"e}l Couturier}{}}
   4 \@writefile{toc}{\author{Jacques Bahi}{}}
   5 \@writefile{loa}{\addvspace {10\p@ }}
   6 \@writefile{toc}{\contentsline {chapter}{\numberline {10}Solving sparse linear systems with GMRES and CG methods on GPU clusters}{215}}
   7 \@writefile{lof}{\addvspace {10\p@ }}
   8 \@writefile{lot}{\addvspace {10\p@ }}
   9 \newlabel{ch12}{{10}{215}}
  10 \@writefile{toc}{\contentsline {section}{\numberline {10.1}Introduction}{215}}
  11 \newlabel{ch12:sec:01}{{10.1}{215}}
  12 \@writefile{toc}{\contentsline {section}{\numberline {10.2}Krylov iterative methods}{216}}
  13 \newlabel{ch12:sec:02}{{10.2}{216}}
  14 \newlabel{ch12:eq:01}{{10.1}{216}}
  15 \newlabel{ch12:eq:02}{{10.2}{216}}
  16 \newlabel{ch12:eq:03}{{10.3}{216}}
  17 \newlabel{ch12:eq:11}{{10.4}{217}}
  18 \@writefile{toc}{\contentsline {subsection}{\numberline {10.2.1}CG method}{217}}
  19 \newlabel{ch12:sec:02.01}{{10.2.1}{217}}
  20 \newlabel{ch12:eq:04}{{10.5}{217}}
  21 \newlabel{ch12:eq:05}{{10.6}{217}}
  22 \newlabel{ch12:eq:06}{{10.7}{217}}
  23 \newlabel{ch12:eq:07}{{10.8}{217}}
  24 \newlabel{ch12:eq:08}{{10.9}{217}}
  25 \newlabel{ch12:eq:09}{{10.10}{217}}
  26 \@writefile{loa}{\contentsline {algocf}{\numberline {9}{\ignorespaces Left-preconditioned CG method\relax }}{218}}
  27 \newlabel{ch12:alg:01}{{9}{218}}
  28 \newlabel{ch12:eq:10}{{10.11}{218}}
  29 \@writefile{toc}{\contentsline {subsection}{\numberline {10.2.2}GMRES method}{219}}
  30 \newlabel{ch12:sec:02.02}{{10.2.2}{219}}
  31 \newlabel{ch12:eq:12}{{10.12}{219}}
  32 \newlabel{ch12:eq:13}{{10.13}{219}}
  33 \newlabel{ch12:eq:14}{{10.14}{219}}
  34 \newlabel{ch12:eq:15}{{10.15}{219}}
  35 \newlabel{ch12:eq:16}{{10.16}{219}}
  36 \newlabel{ch12:eq:17}{{10.17}{219}}
  37 \newlabel{ch12:eq:18}{{10.18}{219}}
  38 \newlabel{ch12:eq:19}{{10.19}{219}}
  39 \@writefile{loa}{\contentsline {algocf}{\numberline {10}{\ignorespaces Left-preconditioned GMRES method with restarts\relax }}{220}}
  40 \newlabel{ch12:alg:02}{{10}{220}}
  41 \@writefile{toc}{\contentsline {section}{\numberline {10.3}Parallel implementation on a GPU cluster}{221}}
  42 \newlabel{ch12:sec:03}{{10.3}{221}}
  43 \@writefile{toc}{\contentsline {subsection}{\numberline {10.3.1}Data partitioning}{221}}
  44 \newlabel{ch12:sec:03.01}{{10.3.1}{221}}
  45 \@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}}
  46 \newlabel{ch12:fig:01}{{10.1}{222}}
  47 \@writefile{toc}{\contentsline {subsection}{\numberline {10.3.2}GPU computing}{222}}
  48 \newlabel{ch12:sec:03.02}{{10.3.2}{222}}
  49 \@writefile{toc}{\contentsline {subsection}{\numberline {10.3.3}Data communications}{223}}
  50 \newlabel{ch12:sec:03.03}{{10.3.3}{223}}
  51 \@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}}
  52 \newlabel{ch12:fig:02}{{10.2}{224}}
  53 \@writefile{lof}{\contentsline {figure}{\numberline {10.3}{\ignorespaces Columns reordering of a sparse sub-matrix.\relax }}{225}}
  54 \newlabel{ch12:fig:03}{{10.3}{225}}
  55 \@writefile{toc}{\contentsline {section}{\numberline {10.4}Experimental results}{226}}
  56 \newlabel{ch12:sec:04}{{10.4}{226}}
  57 \@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}}
  58 \newlabel{ch12:fig:04}{{10.4}{226}}
  59 \@writefile{lof}{\contentsline {figure}{\numberline {10.5}{\ignorespaces Sketches of sparse matrices chosen from the Davis collection.\relax }}{227}}
  60 \newlabel{ch12:fig:05}{{10.5}{227}}
  61 \@writefile{lot}{\contentsline {table}{\numberline {10.1}{\ignorespaces Main characteristics of sparse matrices chosen from the Davis collection.\relax }}{227}}
  62 \newlabel{ch12:tab:01}{{10.1}{227}}
  63 \@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}}
  64 \newlabel{ch12:tab:02}{{10.2}{228}}
  65 \@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}}
  66 \newlabel{ch12:tab:03}{{10.3}{228}}
  67 \newlabel{ch12:eq:20}{{10.20}{229}}
  68 \@writefile{lof}{\contentsline {figure}{\numberline {10.6}{\ignorespaces Parallel generation of a large sparse matrix by four computing nodes.\relax }}{230}}
  69 \newlabel{ch12:fig:06}{{10.6}{230}}
  70 \@writefile{lot}{\contentsline {table}{\numberline {10.4}{\ignorespaces Main characteristics of sparse banded matrices generated from those of the Davis collection.\relax }}{230}}
  71 \newlabel{ch12:tab:04}{{10.4}{230}}
  72 \@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}}
  73 \newlabel{ch12:tab:05}{{10.5}{231}}
  74 \@writefile{toc}{\contentsline {section}{\numberline {10.5}Conclusion}{231}}
  75 \newlabel{ch12:sec:05}{{10.5}{231}}
  76 \@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}}
  77 \newlabel{ch12:tab:06}{{10.6}{232}}
  78 \@writefile{toc}{\contentsline {section}{Bibliography}{232}}
  79 \@setckpt{Chapters/chapter12/ch12}{
  80 \setcounter{page}{234}
  81 \setcounter{equation}{22}
  82 \setcounter{enumi}{4}
  83 \setcounter{enumii}{0}
  84 \setcounter{enumiii}{0}
  85 \setcounter{enumiv}{10}
  86 \setcounter{footnote}{0}
  87 \setcounter{mpfootnote}{0}
  88 \setcounter{part}{5}
  89 \setcounter{chapter}{10}
  90 \setcounter{section}{5}
  91 \setcounter{subsection}{0}
  92 \setcounter{subsubsection}{0}
  93 \setcounter{paragraph}{0}
  94 \setcounter{subparagraph}{0}
  95 \setcounter{figure}{6}
  96 \setcounter{table}{6}
  97 \setcounter{numauthors}{0}
  98 \setcounter{parentequation}{8}
  99 \setcounter{subfigure}{0}
 100 \setcounter{lofdepth}{1}
 101 \setcounter{subtable}{0}
 102 \setcounter{lotdepth}{1}
 103 \setcounter{lstnumber}{50}
 104 \setcounter{ContinuedFloat}{0}
 105 \setcounter{AlgoLine}{29}
 106 \setcounter{algocfline}{10}
 107 \setcounter{algocfproc}{10}
 108 \setcounter{algocf}{10}
 109 \setcounter{nprt@mantissa@digitsbefore}{0}
 110 \setcounter{nprt@mantissa@digitsafter}{0}
 111 \setcounter{nprt@exponent@digitsbefore}{0}
 112 \setcounter{nprt@exponent@digitsafter}{0}
 113 \setcounter{nprt@digitsfirstblock}{0}
 114 \setcounter{nprt@blockcnt}{0}
 115 \setcounter{nprt@cntprint}{0}
 116 \setcounter{proposition}{1}
 117 \setcounter{theorem}{0}
 118 \setcounter{exercise}{0}
 119 \setcounter{example}{0}
 120 \setcounter{definition}{0}
 121 \setcounter{proof}{1}
 122 \setcounter{lstlisting}{0}
 123 }