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1 \relax 
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}{277}}
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12 \@writefile{toc}{\contentsline {section}{\numberline {12.1}Introduction}{277}}
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14 \@writefile{toc}{\contentsline {section}{\numberline {12.2}Obstacle problems}{278}}
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16 \@writefile{toc}{\contentsline {subsection}{\numberline {12.2.1}Mathematical model}{278}}
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20 \@writefile{toc}{\contentsline {subsection}{\numberline {12.2.2}Discretization}{279}}
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25 \@writefile{toc}{\contentsline {section}{\numberline {12.3}Parallel iterative method}{280}}
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38 \@writefile{toc}{\contentsline {section}{\numberline {12.4}Parallel implementation on a GPU cluster}{283}}
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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 }}{283}}
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42 \@writefile{loa}{\contentsline {algocf}{\numberline {11}{\ignorespaces Parallel solving of the obstacle problem on a GPU cluster\relax }}{284}}
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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 }}{285}}
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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 }}{286}}
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50 \@writefile{lol}{\contentsline {lstlisting}{\numberline {12.1}Skeleton codes of a GPU kernel and a CPU function}{286}}
51 \@writefile{lof}{\contentsline {figure}{\numberline {12.3}{\ignorespaces Matrix constant coefficients in a three-dimensional domain.\relax }}{288}}
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56 \@writefile{lof}{\contentsline {figure}{\numberline {12.4}{\ignorespaces Computation of a vector element with the projected Richardson method.\relax }}{290}}
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60 \@writefile{toc}{\contentsline {section}{\numberline {12.5}Experimental tests on a GPU cluster}{291}}
61 \newlabel{ch13:sec:05}{{12.5}{291}}
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 }}{293}}
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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 }}{293}}
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68 \@writefile{toc}{\contentsline {section}{\numberline {12.6}Red-Black ordering technique}{294}}
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76 \@writefile{lof}{\contentsline {figure}{\numberline {12.6}{\ignorespaces Red-Black ordering for computing the iterate vector elements in a three-dimensional space.\relax }}{296}}
77 \@writefile{lof}{\contentsline {subfigure}{\numberline{(a)}{\ignorespaces {Red-Black ordering on x, y and z axises}}}{296}}
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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 }}{298}}
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83 \@writefile{toc}{\contentsline {section}{\numberline {12.7}Conclusion}{298}}
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85 \@writefile{toc}{\contentsline {section}{Bibliography}{299}}
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