new

[book_gpu.git] / BookGPU / Chapters / chapter12 / ch12.tex

diff --git a/BookGPU/Chapters/chapter12/ch12.tex b/BookGPU/Chapters/chapter12/ch12.tex
index 63eae8cdd7bd889df4346b59ce6360d75846e174..576a0cd5e5c4abfc64fc61f57c0112a7e7c1bf53 100755 (executable)
--- a/BookGPU/Chapters/chapter12/ch12.tex
+++ b/BookGPU/Chapters/chapter12/ch12.tex
@@ -5,11 +5,11 @@
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  
 %\chapterauthor{}{}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  
 %\chapterauthor{}{}

-\chapterauthor{Lilia Ziane Khodja}{Femto-ST Institute, University of Franche-Comte, France}
-\chapterauthor{Raphaël Couturier}{Femto-ST Institute, University of Franche-Comte, France}
-\chapterauthor{Jacques Bahi}{Femto-ST Institute, University of Franche-Comte, France}
+\chapterauthor{Lilia Ziane Khodja, Raphaël Couturier and Jacques Bahi}{Femto-ST Institute, University of Franche-Comte, France}
+%\chapterauthor{Raphaël Couturier}{Femto-ST Institute, University of Franche-Comte, France}
+%\chapterauthor{Jacques Bahi}{Femto-ST Institute, University of Franche-Comte, France}

 
 

-\chapter{Solving sparse linear systems with GMRES and CG methods on GPU clusters}
+\chapter[Solving linear systems with GMRES and CG methods on GPU clusters]{Solving sparse linear systems with GMRES and CG methods on GPU clusters}

 \label{ch12}
 
 %%--------------------------%%
 \label{ch12}
 
 %%--------------------------%%


@@ -688,13 +688,13 @@ from the Davis collection. Then, it puts all these copies on the main diagonal o
 diagonal are filled with sub-copies (left-copy and right-copy in Figure~\ref{ch12:fig:06}) of the same
 initial matrix.
 
 diagonal are filled with sub-copies (left-copy and right-copy in Figure~\ref{ch12:fig:06}) of the same
 initial matrix.
 

-\begin{figure}
+\begin{figure}[htbp]

 \centerline{\includegraphics[scale=0.30]{Chapters/chapter12/figures/generation}}
 \caption{Parallel generation of a large sparse matrix by four computing nodes.}
 \label{ch12:fig:06}
 \end{figure}
 
 \centerline{\includegraphics[scale=0.30]{Chapters/chapter12/figures/generation}}
 \caption{Parallel generation of a large sparse matrix by four computing nodes.}
 \label{ch12:fig:06}
 \end{figure}
 

-\begin{table}[!h]
+\begin{table}[htbp]

 \centering
 \begin{tabular}{|c|c|c|c|}
 \hline
 \centering
 \begin{tabular}{|c|c|c|c|}
 \hline


@@ -729,20 +729,7 @@ initial matrix.
 \label{ch12:tab:04}
 \end{table}
 
 \label{ch12:tab:04}
 \end{table}
 

-We have used the parallel CG and GMRES algorithms for solving sparse linear systems of $25$
-million unknown values. The sparse matrices associated to these linear systems are generated
-from those presented in Table~\ref{ch12:tab:01}. Their main characteristics are given in Table~\ref{ch12:tab:04}.
-Tables~\ref{ch12:tab:05} and~\ref{ch12:tab:06} shows the performances of the parallel CG and
-GMRES solvers, respectively, obtained on a cluster of $24$ CPU cores and on a cluster of $12$
-GPUs. Obviously, we can notice from these tables that solving large sparse linear systems on
-a GPU cluster is more efficient than on a CPU cluster (see relative gains $\tau$). We can also
-notice that the execution times of the CG method, whether in a CPU cluster or in a GPU cluster,
-are better than those of the GMRES method for solving large symmetric linear systems. In fact, the
-CG method is characterized by a better convergence\index{Convergence} rate and a shorter execution
-time of an iteration than those of the GMRES method. Moreover, an iteration of the parallel GMRES
-method requires more data exchanges between computing nodes compared to the parallel CG method.
- 
-\begin{table}
+\begin{table}[htbp]

 \begin{center}
 \begin{tabular}{|c|c|c|c|c|c|c|} 
 \hline
 \begin{center}
 \begin{tabular}{|c|c|c|c|c|c|c|} 
 \hline


@@ -802,6 +789,21 @@ on a cluster of 12 GPUs.}
 \end{center}
 \end{table}
 
 \end{center}
 \end{table}
 

+
+We have used the parallel CG and GMRES algorithms for solving sparse linear systems of $25$
+million unknown values. The sparse matrices associated to these linear systems are generated
+from those presented in Table~\ref{ch12:tab:01}. Their main characteristics are given in Table~\ref{ch12:tab:04}.
+Tables~\ref{ch12:tab:05} and~\ref{ch12:tab:06} shows the performances of the parallel CG and
+GMRES solvers, respectively, obtained on a cluster of $24$ CPU cores and on a cluster of $12$
+GPUs. Obviously, we can notice from these tables that solving large sparse linear systems on
+a GPU cluster is more efficient than on a CPU cluster (see relative gains $\tau$). We can also
+notice that the execution times of the CG method, whether in a CPU cluster or in a GPU cluster,
+are better than those of the GMRES method for solving large symmetric linear systems. In fact, the
+CG method is characterized by a better convergence\index{Convergence} rate and a shorter execution
+time of an iteration than those of the GMRES method. Moreover, an iteration of the parallel GMRES
+method requires more data exchanges between computing nodes compared to the parallel CG method.
+ 
+

 %%--------------------------%%
 %%       SECTION 5          %%
 %%--------------------------%%
 %%--------------------------%%
 %%       SECTION 5          %%
 %%--------------------------%%