X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/book_gpu.git/blobdiff_plain/4f8020b1c6324b056b53b4325cd80d59bb7cf19f..177d75ae3d1a1061fb9caa43de9afca760ca0d1a:/BookGPU/Chapters/chapter5/ch5.tex diff --git a/BookGPU/Chapters/chapter5/ch5.tex b/BookGPU/Chapters/chapter5/ch5.tex index cbf81f3..1d3d957 100644 --- a/BookGPU/Chapters/chapter5/ch5.tex +++ b/BookGPU/Chapters/chapter5/ch5.tex @@ -174,13 +174,16 @@ where $u(x,y,t)$ is the unknown heat distribution, $\kappa$ is a heat conductivi u(x,y,t_0) = \sin(\pi x)\,\sin(\pi y), & \qquad (x,y) \in \Omega. \end{align} An illustrative example of the numerical solution to the heat problem, using \eqref{ch5:eq:heatinit} as the initial condition is given in Figure \ref{ch5:fig:heatsolution}. -\begin{figure}[!htb] +\begin{figure}[!htbp] \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}} + \setlength\figureheight{0.3\textwidth} % + \subfigure[$t=0.00s$]%{\input{Chapters/chapter5/figures/HeatSolution0.tikz}} +{\includegraphics[width=0.48\textwidth]{Chapters/chapter5/figures/HeatSolution0_conv.pdf}} + \subfigure[$t=0.05s$]%{\input{Chapters/chapter5/figures/HeatSolution0.049307.tikz}} +{\includegraphics[width=0.48\textwidth]{Chapters/chapter5/figures/HeatSolution0_049307_conv.pdf}} %\subfigure[$t=0.10s$]{\input{Chapters/chapter5/figures/HeatSolution0.099723.tikz}} +{\includegraphics[width=0.48\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. A speci \putbib[Chapters/chapter5/biblio5] % Reset lst label and caption -\lstset{label=,caption=} \ No newline at end of file +\lstset{label=,caption=}