BookGPU/Chapters/chapter13/ch13.aux

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   2 \@writefile{toc}{\author{Lilia Ziane Khodja}{}}
   3 \@writefile{toc}{\author{Ming Chau}{}}
   4 \@writefile{toc}{\author{Rapha\IeC {\"e}l Couturier}{}}
   5 \@writefile{toc}{\author{Pierre Spit\IeC {\'e}ri}{}}
   6 \@writefile{toc}{\author{Jacques Bahi}{}}
   7 \@writefile{loa}{\addvspace {10\p@ }}
   8 \@writefile{toc}{\contentsline {chapter}{\numberline {12}Solving sparse nonlinear systems of obstacle problems on GPU clusters}{279}}
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  12 \@writefile{toc}{\contentsline {section}{\numberline {12.1}Introduction}{279}}
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  14 \@writefile{toc}{\contentsline {section}{\numberline {12.2}Obstacle problems}{280}}
  15 \newlabel{ch13:sec:02}{{12.2}{280}}
  16 \@writefile{toc}{\contentsline {subsection}{\numberline {12.2.1}Mathematical model}{280}}
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  20 \@writefile{toc}{\contentsline {subsection}{\numberline {12.2.2}Discretization}{281}}
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  25 \@writefile{toc}{\contentsline {section}{\numberline {12.3}Parallel iterative method}{282}}
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  38 \@writefile{toc}{\contentsline {section}{\numberline {12.4}Parallel implementation on a GPU cluster}{285}}
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  40 \@writefile{lof}{\contentsline {figure}{\numberline {12.1}{\ignorespaces Data partitioning of a problem to be solved among $S=3\times 4$ computing nodes.\relax }}{285}}
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  42 \@writefile{loa}{\contentsline {algocf}{\numberline {11}{\ignorespaces Parallel solving of the obstacle problem on a GPU cluster\relax }}{286}}
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  45 \@writefile{loa}{\contentsline {algocf}{\numberline {12}{\ignorespaces Parallel iterative solving of the nonlinear systems on a GPU cluster ($Solve()$ function)\relax }}{287}}
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  47 \@writefile{lof}{\contentsline {figure}{\numberline {12.2}{\ignorespaces Decomposition of a sub-problem in a GPU into $nz$ slices.\relax }}{288}}
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  50 \@writefile{lol}{\contentsline {lstlisting}{\numberline {12.1}Skeleton codes of a GPU kernel and a CPU function}{288}}
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  52 \@writefile{lof}{\contentsline {figure}{\numberline {12.3}{\ignorespaces Matrix constant coefficients in a three-dimensional domain.\relax }}{290}}
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  55 \@writefile{lol}{\contentsline {lstlisting}{\numberline {12.2}GPU kernels of the projected Richardson method}{290}}
  56 \@writefile{lof}{\contentsline {figure}{\numberline {12.4}{\ignorespaces Computation of a vector element with the projected Richardson method.\relax }}{291}}
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  59 \@writefile{lol}{\contentsline {lstlisting}{\numberline {12.3}Memory access to the cache texture memory}{292}}
  60 \@writefile{toc}{\contentsline {section}{\numberline {12.5}Experimental tests on a GPU cluster}{293}}
  61 \newlabel{ch13:sec:05}{{12.5}{293}}
  62 \@writefile{lof}{\contentsline {figure}{\numberline {12.5}{\ignorespaces GPU cluster of tests composed of 12 computing nodes (six machines, each with two GPUs.\relax }}{294}}
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  64 \@writefile{lot}{\contentsline {table}{\numberline {12.1}{\ignorespaces Execution times in seconds of the parallel projected Richardson method implemented on a cluster of 24 CPU cores.\relax }}{295}}
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  68 \@writefile{toc}{\contentsline {section}{\numberline {12.6}Red-Black ordering technique}{296}}
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  70 \newlabel{ch13:fig:06.01}{{12.6(a)}{297}}
  71 \newlabel{sub@ch13:fig:06.01}{{(a)}{297}}
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  74 \@writefile{lof}{\contentsline {figure}{\numberline {12.6}{\ignorespaces Red-Black ordering for computing the iterate vector elements in a three-dimensional space.\relax }}{297}}
  75 \@writefile{lof}{\contentsline {subfigure}{\numberline{(a)}{\ignorespaces {Red-Black ordering on x, y and z axises}}}{297}}
  76 \@writefile{lof}{\contentsline {subfigure}{\numberline{(b)}{\ignorespaces {Red-Black ordering on y axis}}}{297}}
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  78 \@writefile{lol}{\contentsline {lstlisting}{\numberline {12.4}GPU kernels of the projected Richardson method using the red-black technique}{297}}
  79 \@writefile{lot}{\contentsline {table}{\numberline {12.3}{\ignorespaces Execution times in seconds of the parallel projected Richardson method using read-black ordering technique implemented on a cluster of 12 GPUs.\relax }}{299}}
  80 \newlabel{ch13:tab:03}{{12.3}{299}}
  81 \@writefile{lof}{\contentsline {figure}{\numberline {12.7}{\ignorespaces Weak scaling of both synchronous and asynchronous algorithms of the projected Richardson method using red-black ordering technique.\relax }}{300}}
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  83 \@writefile{toc}{\contentsline {section}{\numberline {12.7}Conclusion}{300}}
  84 \newlabel{ch13:sec:07}{{12.7}{300}}
  85 \@writefile{toc}{\contentsline {section}{Bibliography}{301}}
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