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 {12}Solving sparse linear systems with GMRES and CG methods on GPU clusters}{293}}
   7 \@writefile{lof}{\addvspace {10\p@ }}
   8 \@writefile{lot}{\addvspace {10\p@ }}
   9 \newlabel{ch12}{{12}{293}}
  10 \@writefile{toc}{\contentsline {section}{\numberline {12.1}Introduction}{293}}
  11 \newlabel{ch12:sec:01}{{12.1}{293}}
  12 \@writefile{toc}{\contentsline {section}{\numberline {12.2}Krylov iterative methods}{294}}
  13 \newlabel{ch12:sec:02}{{12.2}{294}}
  14 \newlabel{ch12:eq:01}{{12.1}{294}}
  15 \newlabel{ch12:eq:02}{{12.2}{294}}
  16 \newlabel{ch12:eq:03}{{12.3}{294}}
  17 \newlabel{ch12:eq:11}{{12.4}{295}}
  18 \@writefile{toc}{\contentsline {subsection}{\numberline {12.2.1}CG method}{295}}
  19 \newlabel{ch12:sec:02.01}{{12.2.1}{295}}
  20 \newlabel{ch12:eq:04}{{12.5}{295}}
  21 \newlabel{ch12:eq:05}{{12.6}{295}}
  22 \newlabel{ch12:eq:06}{{12.7}{295}}
  23 \newlabel{ch12:eq:07}{{12.8}{295}}
  24 \newlabel{ch12:eq:08}{{12.9}{295}}
  25 \newlabel{ch12:eq:09}{{12.10}{295}}
  26 \@writefile{loa}{\contentsline {algocf}{\numberline {14}{\ignorespaces Left-preconditioned CG method\relax }}{296}}
  27 \newlabel{ch12:alg:01}{{14}{296}}
  28 \newlabel{ch12:eq:10}{{12.11}{296}}
  29 \@writefile{toc}{\contentsline {subsection}{\numberline {12.2.2}GMRES method}{297}}
  30 \newlabel{ch12:sec:02.02}{{12.2.2}{297}}
  31 \newlabel{ch12:eq:12}{{12.12}{297}}
  32 \newlabel{ch12:eq:13}{{12.13}{297}}
  33 \newlabel{ch12:eq:14}{{12.14}{297}}
  34 \newlabel{ch12:eq:15}{{12.15}{297}}
  35 \newlabel{ch12:eq:16}{{12.16}{297}}
  36 \newlabel{ch12:eq:17}{{12.17}{297}}
  37 \newlabel{ch12:eq:18}{{12.18}{297}}
  38 \newlabel{ch12:eq:19}{{12.19}{297}}
  39 \@writefile{loa}{\contentsline {algocf}{\numberline {15}{\ignorespaces Left-preconditioned GMRES method with restarts\relax }}{298}}
  40 \newlabel{ch12:alg:02}{{15}{298}}
  41 \@writefile{toc}{\contentsline {section}{\numberline {12.3}Parallel implementation on a GPU cluster}{299}}
  42 \newlabel{ch12:sec:03}{{12.3}{299}}
  43 \@writefile{toc}{\contentsline {subsection}{\numberline {12.3.1}Data partitioning}{299}}
  44 \newlabel{ch12:sec:03.01}{{12.3.1}{299}}
  45 \@writefile{lof}{\contentsline {figure}{\numberline {12.1}{\ignorespaces A data partitioning of the sparse matrix $A$, the solution vector $x$ and the right-hand side $b$ into four portions.\relax }}{300}}
  46 \newlabel{ch12:fig:01}{{12.1}{300}}
  47 \@writefile{toc}{\contentsline {subsection}{\numberline {12.3.2}GPU computing}{300}}
  48 \newlabel{ch12:sec:03.02}{{12.3.2}{300}}
  49 \@writefile{toc}{\contentsline {subsection}{\numberline {12.3.3}Data communications}{301}}
  50 \newlabel{ch12:sec:03.03}{{12.3.3}{301}}
  51 \@writefile{lof}{\contentsline {figure}{\numberline {12.2}{\ignorespaces Data exchanges between \textit  {Node 1} and its neighbors \textit  {Node 0}, \textit  {Node 2} and \textit  {Node 3}.\relax }}{302}}
  52 \newlabel{ch12:fig:02}{{12.2}{302}}
  53 \@writefile{lof}{\contentsline {figure}{\numberline {12.3}{\ignorespaces Columns reordering of a sparse sub-matrix.\relax }}{303}}
  54 \newlabel{ch12:fig:03}{{12.3}{303}}
  55 \@writefile{toc}{\contentsline {section}{\numberline {12.4}Experimental results}{304}}
  56 \newlabel{ch12:sec:04}{{12.4}{304}}
  57 \@writefile{lof}{\contentsline {figure}{\numberline {12.4}{\ignorespaces General scheme of the GPU cluster of tests composed of six machines, each with two GPUs.\relax }}{304}}
  58 \newlabel{ch12:fig:04}{{12.4}{304}}
  59 \@writefile{lof}{\contentsline {figure}{\numberline {12.5}{\ignorespaces Sketches of sparse matrices chosen from the Davis collection.\relax }}{305}}
  60 \newlabel{ch12:fig:05}{{12.5}{305}}
  61 \@writefile{lot}{\contentsline {table}{\numberline {12.1}{\ignorespaces Main characteristics of sparse matrices chosen from the Davis collection.\relax }}{305}}
  62 \newlabel{ch12:tab:01}{{12.1}{305}}
  63 \@writefile{lot}{\contentsline {table}{\numberline {12.2}{\ignorespaces Performances of the parallel CG method on a cluster of 24 CPU cores vs. on a cluster of 12 GPUs.\relax }}{306}}
  64 \newlabel{ch12:tab:02}{{12.2}{306}}
  65 \@writefile{lot}{\contentsline {table}{\numberline {12.3}{\ignorespaces Performances of the parallel GMRES method on a cluster 24 CPU cores vs. on cluster of 12 GPUs.\relax }}{306}}
  66 \newlabel{ch12:tab:03}{{12.3}{306}}
  67 \newlabel{ch12:eq:20}{{12.20}{307}}
  68 \@writefile{lof}{\contentsline {figure}{\numberline {12.6}{\ignorespaces Parallel generation of a large sparse matrix by four computing nodes.\relax }}{308}}
  69 \newlabel{ch12:fig:06}{{12.6}{308}}
  70 \@writefile{lot}{\contentsline {table}{\numberline {12.4}{\ignorespaces Main characteristics of sparse banded matrices generated from those of the Davis collection.\relax }}{308}}
  71 \newlabel{ch12:tab:04}{{12.4}{308}}
  72 \@writefile{lot}{\contentsline {table}{\numberline {12.5}{\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 }}{309}}
  73 \newlabel{ch12:tab:05}{{12.5}{309}}
  74 \@writefile{toc}{\contentsline {section}{\numberline {12.5}Conclusion}{309}}
  75 \newlabel{ch12:sec:05}{{12.5}{309}}
  76 \@writefile{lot}{\contentsline {table}{\numberline {12.6}{\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 }}{310}}
  77 \newlabel{ch12:tab:06}{{12.6}{310}}
  78 \@writefile{toc}{\contentsline {section}{Bibliography}{310}}
  79 \@setckpt{Chapters/chapter12/ch12}{
  80 \setcounter{page}{312}
  81 \setcounter{equation}{22}
  82 \setcounter{enumi}{2}
  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}{12}
  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}{46}
  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}{15}
 107 \setcounter{algocfproc}{15}
 108 \setcounter{algocf}{15}
 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 }