X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/book_gpu.git/blobdiff_plain/2373d6731790822c6e738cfa54aec1ccaf802222..8db670a863cf32ab3e5fbd99ecc161d6317c763f:/BookGPU/Chapters/chapter12/ch12.tex?ds=sidebyside

diff --git a/BookGPU/Chapters/chapter12/ch12.tex b/BookGPU/Chapters/chapter12/ch12.tex
index 254c0cb..8b869b3 100755
--- a/BookGPU/Chapters/chapter12/ch12.tex
+++ b/BookGPU/Chapters/chapter12/ch12.tex
@@ -1,4 +1,4 @@
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+1%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %%                          %%
 %%       CHAPTER 12         %%
 %%                          %%
@@ -729,19 +729,6 @@ initial matrix.
 \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{center}
 \begin{tabular}{|c|c|c|c|c|c|c|} 
@@ -802,6 +789,21 @@ on a cluster of 12 GPUs.}
 \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          %%
 %%--------------------------%%