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BookGPU/Chapters/chapter5/figures/MultiGPUAlphaPerformanceTeslaM2050_N16777216_conv.pdf create mode 100644 BookGPU/Chapters/chapter5/figures/MultiGPUAlphaPerformanceTeslaM2050_N16777216_conv.ps create mode 100644 BookGPU/Chapters/chapter5/figures/poisson_performance_conv.pdf create mode 100644 BookGPU/Chapters/chapter5/figures/poisson_performance_conv.ps create mode 100644 BookGPU/Chapters/chapter5/figures/poisson_solution_conv.pdf create mode 100644 BookGPU/Chapters/chapter5/figures/poisson_solution_conv.ps diff --git a/BookGPU/BookGPU.tex b/BookGPU/BookGPU.tex index 23267c5..eaa9c44 100755 --- a/BookGPU/BookGPU.tex +++ b/BookGPU/BookGPU.tex @@ -147,7 +147,7 @@ \makeindex -% \includeonly{Chapters/chapter7/ch7} +%\includeonly{Chapters/chapter5/ch5} \begin{document} @@ -183,7 +183,7 @@ \part{Image processing} \include{Chapters/chapter3/ch3} \part{Software development} -\include{Chapters/chapter5/ch5}% HeatSolution0.049307.pdf HeatSolution0.pdf ... +\include{Chapters/chapter5/ch5}% lib HeatSolution0.049307.pdf HeatSolution0.pdf ... \include{Chapters/chapter6/ch6} \part{Optimization} \include{Chapters/chapter8/ch8} diff --git a/BookGPU/Chapters/chapter12/ch12.aux b/BookGPU/Chapters/chapter12/ch12.aux index 5841c60..f4f6c5c 100644 --- a/BookGPU/Chapters/chapter12/ch12.aux +++ b/BookGPU/Chapters/chapter12/ch12.aux @@ -3,81 +3,81 @@ \@writefile{toc}{\author{Rapha\IeC {\"e}l Couturier}{}} \@writefile{toc}{\author{Jacques Bahi}{}} \@writefile{loa}{\addvspace {10\p@ }} -\@writefile{toc}{\contentsline {chapter}{\numberline {12}Solving sparse linear systems with GMRES and CG methods on GPU clusters}{293}} +\@writefile{toc}{\contentsline {chapter}{\numberline {12}Solving sparse linear systems with GMRES and CG methods on GPU clusters}{295}} \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} -\newlabel{ch12}{{12}{293}} -\@writefile{toc}{\contentsline {section}{\numberline {12.1}Introduction}{293}} -\newlabel{ch12:sec:01}{{12.1}{293}} 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\setcounter{enumi}{3} \setcounter{enumii}{0} diff --git a/BookGPU/Chapters/chapter5/ch5.tex b/BookGPU/Chapters/chapter5/ch5.tex index cbf81f3..1c5da65 100644 --- a/BookGPU/Chapters/chapter5/ch5.tex +++ b/BookGPU/Chapters/chapter5/ch5.tex @@ -178,9 +178,12 @@ An illustrative example of the numerical solution to the heat problem, using \eq \begin{center} \setlength\figurewidth{0.3\textwidth} % \setlength\figureheight{0.32\textwidth} % - \subfigure[$t=0.00s$]{\input{Chapters/chapter5/figures/HeatSolution0.tikz}} - \subfigure[$t=0.05s$]{\input{Chapters/chapter5/figures/HeatSolution0.049307.tikz}} + \subfigure[$t=0.00s$]%{\input{Chapters/chapter5/figures/HeatSolution0.tikz}} +{\includegraphics[width=0.5\textwidth]{Chapters/chapter5/figures/HeatSolution0_conv.pdf}} + \subfigure[$t=0.05s$]%{\input{Chapters/chapter5/figures/HeatSolution0.049307.tikz}} +{\includegraphics[width=0.5\textwidth]{Chapters/chapter5/figures/HeatSolution0_049307_conv.pdf}} %\subfigure[$t=0.10s$]{\input{Chapters/chapter5/figures/HeatSolution0.099723.tikz}} +{\includegraphics[width=0.5\textwidth]{Chapters/chapter5/figures/HeatSolution0_099723_conv.pdf}} \end{center} \caption{Discrete solution at times $t=0s$ and $t=0.05s$, using \eqref{ch5:eq:heatinit} as initial condition and a small $20\times20$ numerical grid.}\label{ch5:fig:heatsolution} \end{figure} @@ -263,7 +266,8 @@ Solution times for the heat conduction problem is in itself not very interesting \setlength\figurewidth{0.4\textwidth} \begin{center} {\small -\input{Chapters/chapter5/figures/AlphaPerformanceGTX590_N16777216.tikz} +%\input{Chapters/chapter5/figures/AlphaPerformanceGTX590_N16777216.tikz} +{\includegraphics[width=0.5\textwidth]{Chapters/chapter5/figures/AlphaPerformanceGTX590_N16777216_conv.pdf}} } \end{center} \caption{Single and double precision floating point operations per second for a two dimensional stencil operator on a numerical grid of size $4096^2$. Various stencil sizes are used $\alpha=1,2,3,4$, equivalent to $5$pt, $9$pt, $13$pt, and $17$pt stencils. Test environment 1.}\label{ch5:fig:stencilperformance} @@ -386,10 +390,14 @@ Defect correction in combination with multigrid preconditioning, enables efficie \setlength\figurewidth{0.33\textwidth} \begin{center} \subfigure[Convergence history for the conjugate gradient and multigrid methods, for two different problem sizes.]{\label{ch5:fig:poissonconvergence:a} - {\scriptsize \input{Chapters/chapter5/figures/ConvergenceMGvsCG.tikz}} -} \hspace{0.2cm}% + %{\scriptsize \input{Chapters/chapter5/figures/ConvergenceMGvsCG.tikz}} + {\includegraphics[width=0.5\textwidth]{Chapters/chapter5/figures/ConvergenceMGvsCG_conv.pdf}} +} + + \hspace{0.2cm}% \subfigure[Defect correction convergence history for three different stencil sizes.]{\label{ch5:fig:poissonconvergence:b} - {\scriptsize \input{Chapters/chapter5/figures/ConvergenceDC.tikz}} + %{\scriptsize \input{Chapters/chapter5/figures/ConvergenceDC.tikz}} + {\includegraphics[width=0.5\textwidth]{Chapters/chapter5/figures/ConvergenceDC_conv.pdf}} } \end{center} \caption{Algorithmic performance for the conjugate gradient, multigrid, and defect correction methods, measured in terms of the relative residual per iteration.}\label{ch5:fig:poissonconvergence} @@ -449,11 +457,13 @@ Distributed performance for the finite difference stencil operation is illustrat \setlength\figurewidth{0.55\textwidth} \begin{center} \subfigure[Absolute timings, $\alpha=3$.]{ - {\small\input{Chapters/chapter5/figures/MultiGPUAlpha3TimingsTeslaM2050.tikz}} + %{\small\input{Chapters/chapter5/figures/MultiGPUAlpha3TimingsTeslaM2050.tikz}} + {\includegraphics[width=0.6\textwidth]{Chapters/chapter5/figures/MultiGPUAlpha3TimingsTeslaM2050_conv.pdf}} \label{ch5:fig:multigpu:a} } \subfigure[Performance at $N=4069^2$, single precision.]{ - {\small\input{Chapters/chapter5/figures/MultiGPUAlphaPerformanceTeslaM2050_N16777216.tikz}} + % {\small\input{Chapters/chapter5/figures/MultiGPUAlphaPerformanceTeslaM2050_N16777216.tikz}} +{\includegraphics[width=0.6\textwidth]{Chapters/chapter5/figures/MultiGPUAlphaPerformanceTeslaM2050_N16777216_conv.pdf}} \label{ch5:fig:multigpu:b} } \end{center} @@ -623,4 +633,4 @@ from the Danish Research Council for Technology and Production Sciences. 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pdfFillOP setoverprint + /pdfLastFill true def /pdfLastStroke false def + } if +} def +/sCol { + pdfLastStroke not { + pdfStrokeCS setcolorspace + pdfStroke aload pop pdfStrokeXform setcolor + pdfStrokeOP setoverprint + /pdfLastStroke true def /pdfLastFill false def + } if +} def +% build a font +/pdfMakeFont { + 4 3 roll findfont + 4 2 roll matrix scale makefont + dup length dict begin + { 1 index /FID ne { def } { pop pop } ifelse } forall + /Encoding exch def + currentdict + end + definefont pop +} def +/pdfMakeFont16 { + exch findfont + dup length dict begin + { 1 index /FID ne { def } { pop pop } ifelse } forall + /WMode exch def + currentdict + end + definefont pop +} def +% graphics state operators +/q { gsave pdfDictSize dict begin } def +/Q { + end grestore + /pdfLastFill where { + pop + pdfLastFill { + pdfFillOP setoverprint + } { + pdfStrokeOP setoverprint + } ifelse + } if +} def +/cm { concat } def +/d { setdash } def +/i { setflat } def +/j { setlinejoin } def +/J { setlinecap } def +/M { setmiterlimit } def +/w { setlinewidth } def +% path segment operators +/m { moveto } def +/l { lineto } def +/c { curveto } def +/re { 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } def +/h { closepath } def +% path painting operators +/S { sCol stroke } def +/Sf { fCol stroke } def +/f { fCol fill } def +/f* { fCol eofill } def +% clipping operators +/W { clip newpath } def +/W* { eoclip newpath } def +/Ws { strokepath clip newpath } def +% text state operators +/Tc { /pdfCharSpacing exch def } def +/Tf { dup /pdfFontSize exch def + dup pdfHorizScaling mul exch matrix scale + pdfTextMat matrix concatmatrix dup 4 0 put dup 5 0 put + exch findfont exch makefont setfont } def +/Tr { /pdfTextRender exch def } def +/Tp { /pdfPatternCS exch def } def +/Ts { /pdfTextRise exch def } def +/Tw { /pdfWordSpacing exch def } def +/Tz { /pdfHorizScaling exch def } def +% text positioning operators +/Td { pdfTextMat transform moveto } def +/Tm { /pdfTextMat exch def } def +% text string operators +/cshow where { + pop + /cshow2 { + dup { + pop pop + 1 string dup 0 3 index put 3 index exec + } exch cshow + pop pop + } def +}{ + /cshow2 { + currentfont /FontType get 0 eq { + 0 2 2 index length 1 sub { + 2 copy get exch 1 add 2 index exch get + 2 copy exch 256 mul add + 2 string dup 0 6 5 roll put dup 1 5 4 roll put + 3 index exec + } for + } { + dup { + 1 string dup 0 3 index put 3 index exec + } forall + } ifelse + pop pop + } def +} ifelse +/awcp { + exch { + false charpath + 5 index 5 index rmoveto + 6 index eq { 7 index 7 index rmoveto } if + } exch cshow2 + 6 {pop} repeat +} def +/Tj { + fCol + 1 index stringwidth pdfTextMat idtransform pop + sub 1 index length dup 0 ne { div } { pop pop 0 } ifelse + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16 { + fCol + 2 index stringwidth pdfTextMat idtransform pop + sub exch div + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16V { + fCol + 2 index stringwidth pdfTextMat idtransform exch pop + sub exch div + 0 pdfWordSpacing pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing add 0 exch + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj1 { + 0 pdfTextRise pdfTextMat dtransform rmoveto + currentpoint 8 2 roll + pdfTextRender 1 and 0 eq pdfPatternCS not and { + 6 copy awidthshow + } if + pdfTextRender 3 and dup 1 eq exch 2 eq or { + 7 index 7 index moveto + 6 copy + currentfont /FontType get 3 eq { fCol } { sCol } ifelse + false awcp currentpoint stroke moveto + } if + pdfTextRender 4 and 0 ne pdfPatternCS or { + 8 6 roll moveto + false awcp + /pdfTextClipPath [ pdfTextClipPath aload pop + {/moveto cvx} + {/lineto cvx} + {/curveto cvx} + {/closepath cvx} + pathforall ] def + currentpoint newpath moveto + } { + 8 {pop} repeat + } 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Operating System: Microsoft Windows Vista. +%%LanguageLevel: 2 +%%DocumentSuppliedResources: (atend) +%%DocumentMedia: plain 432 380 0 () () +%%BoundingBox: 0 0 432 380 +%%Pages: 1 +%%EndComments +%%BeginDefaults +%%PageMedia: plain +%%EndDefaults +%%BeginProlog +%%BeginResource: procset xpdf 3.00 0 +%%Copyright: Copyright 1996-2004 Glyph & Cog, LLC +/xpdf 75 dict def xpdf begin +% PDF special state +/pdfDictSize 15 def +/pdfSetup { + 3 1 roll 2 array astore + /setpagedevice where { + pop 3 dict begin + /PageSize exch def + /ImagingBBox null def + /Policies 1 dict dup begin /PageSize 3 def end def + { /Duplex true def } if + currentdict end setpagedevice + } { + pop pop + } ifelse +} def +/pdfStartPage { + pdfDictSize dict begin + /pdfFillCS [] def + /pdfFillXform {} def + /pdfStrokeCS [] def + /pdfStrokeXform {} def + /pdfFill [0] def + /pdfStroke [0] def + /pdfFillOP false def + /pdfStrokeOP false def + /pdfLastFill false def + /pdfLastStroke false def + /pdfTextMat [1 0 0 1 0 0] def 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pdfFillOP setoverprint + /pdfLastFill true def /pdfLastStroke false def + } if +} def +/sCol { + pdfLastStroke not { + pdfStrokeCS setcolorspace + pdfStroke aload pop pdfStrokeXform setcolor + pdfStrokeOP setoverprint + /pdfLastStroke true def /pdfLastFill false def + } if +} def +% build a font +/pdfMakeFont { + 4 3 roll findfont + 4 2 roll matrix scale makefont + dup length dict begin + { 1 index /FID ne { def } { pop pop } ifelse } forall + /Encoding exch def + currentdict + end + definefont pop +} def +/pdfMakeFont16 { + exch findfont + dup length dict begin + { 1 index /FID ne { def } { pop pop } ifelse } forall + /WMode exch def + currentdict + end + definefont pop +} def +% graphics state operators +/q { gsave pdfDictSize dict begin } def +/Q { + end grestore + /pdfLastFill where { + pop + pdfLastFill { + pdfFillOP setoverprint + } { + pdfStrokeOP setoverprint + } ifelse + } if +} def +/cm { concat } def +/d { setdash } def +/i { setflat } def +/j { setlinejoin } def +/J { setlinecap } def +/M { setmiterlimit } def +/w { setlinewidth } def +% path segment operators +/m { moveto } def +/l { lineto } def +/c { curveto } def +/re { 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } def +/h { closepath } def +% path painting operators +/S { sCol stroke } def +/Sf { fCol stroke } def +/f { fCol fill } def +/f* { fCol eofill } def +% clipping operators +/W { clip newpath } def +/W* { eoclip newpath } def +/Ws { strokepath clip newpath } def +% text state operators +/Tc { /pdfCharSpacing exch def } def +/Tf { dup /pdfFontSize exch def + dup pdfHorizScaling mul exch matrix scale + pdfTextMat matrix concatmatrix dup 4 0 put dup 5 0 put + exch findfont exch makefont setfont } def +/Tr { /pdfTextRender exch def } def +/Tp { /pdfPatternCS exch def } def +/Ts { /pdfTextRise exch def } def +/Tw { /pdfWordSpacing exch def } def +/Tz { /pdfHorizScaling exch def } def +% text positioning operators +/Td { pdfTextMat transform moveto } def +/Tm { /pdfTextMat exch def } def +% text string operators +/cshow where { + pop + /cshow2 { + dup { + pop pop + 1 string dup 0 3 index put 3 index exec + } exch cshow + pop pop + } def +}{ + /cshow2 { + currentfont /FontType get 0 eq { + 0 2 2 index length 1 sub { + 2 copy get exch 1 add 2 index exch get + 2 copy exch 256 mul add + 2 string dup 0 6 5 roll put dup 1 5 4 roll put + 3 index exec + } for + } { + dup { + 1 string dup 0 3 index put 3 index exec + } forall + } ifelse + pop pop + } def +} ifelse +/awcp { + exch { + false charpath + 5 index 5 index rmoveto + 6 index eq { 7 index 7 index rmoveto } if + } exch cshow2 + 6 {pop} repeat +} def +/Tj { + fCol + 1 index stringwidth pdfTextMat idtransform pop + sub 1 index length dup 0 ne { div } { pop pop 0 } ifelse + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16 { + fCol + 2 index stringwidth pdfTextMat idtransform pop + sub exch div + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16V { + fCol + 2 index stringwidth pdfTextMat idtransform exch pop + sub exch div + 0 pdfWordSpacing pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing add 0 exch + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj1 { + 0 pdfTextRise pdfTextMat dtransform rmoveto + currentpoint 8 2 roll + pdfTextRender 1 and 0 eq pdfPatternCS not and { + 6 copy awidthshow + } if + pdfTextRender 3 and dup 1 eq exch 2 eq or { + 7 index 7 index moveto + 6 copy + currentfont /FontType get 3 eq { fCol } { sCol } ifelse + false awcp currentpoint stroke moveto + } if + pdfTextRender 4 and 0 ne pdfPatternCS or { + 8 6 roll moveto + false awcp + /pdfTextClipPath [ pdfTextClipPath aload pop + {/moveto cvx} + {/lineto cvx} + {/curveto cvx} + {/closepath cvx} + pathforall ] def + currentpoint newpath moveto + } { + 8 {pop} repeat + } 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+/axialCol { + dup 0 lt { + pop t0 + } { + dup 1 gt { + pop t1 + } { + dt mul t0 add + } ifelse + } ifelse + func n array astore +} def +/axialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index axialCol 2 index axialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index axialSH + exch 3 2 roll axialSH + } { + pop 2 copy add 0.5 mul + axialCol sc + exch dup dx mul x0 add exch dy mul y0 add + 3 2 roll dup dx mul x0 add exch dy mul y0 add + dx abs dy abs ge { + 2 copy yMin sub dy mul dx div add yMin m + yMax sub dy mul dx div add yMax l + 2 copy yMax sub dy mul dx div add yMax l + yMin sub dy mul dx div add yMin l + h f* + } { + exch 2 copy xMin sub dx mul dy div add xMin exch m + xMax sub dx mul dy div add xMax exch l + exch 2 copy xMax sub dx mul dy div add xMax exch l + xMin sub dx mul dy div add xMin exch l + h f* + } ifelse + } ifelse +} def +/radialCol { + dup t0 lt { + pop t0 + } { + dup t1 gt { + pop t1 + } if + } ifelse + func n array astore +} def +/radialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index dt mul t0 add radialCol + 2 index dt mul t0 add radialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index radialSH + exch 3 2 roll radialSH + } { + pop 2 copy add 0.5 mul dt mul t0 add + radialCol sc + encl { + exch dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + 0 360 arc h + dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + 360 0 arcn h f + } { + 2 copy + dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + a1 a2 arcn + dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + a2 a1 arcn h + dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + a1 a2 arc + dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + a2 a1 arc h f + } ifelse + } ifelse +} def +end +%%EndResource +%%EndProlog +%%BeginSetup +xpdf begin +/F8_0 /Courier 1 1 +[ 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