From 2e01ef1240fcecca4313cea0cb013a8c0b09f9f5 Mon Sep 17 00:00:00 2001 From: couturie Date: Fri, 8 May 2015 11:50:36 +0200 Subject: [PATCH] modif 5.4.5 --- paper.tex | 25 ++++++++++--------------- 1 file changed, 10 insertions(+), 15 deletions(-) diff --git a/paper.tex b/paper.tex index 81afcf5..8126583 100644 --- a/paper.tex +++ b/paper.tex @@ -725,7 +725,7 @@ of $40\%$ which is only around $24\%$ for the classical GMRES. \hline Grid Architecture & 4 $\times$ 8\\ %\hline Inter Network & $bw$=1Gbs - $lat$=5.10$^{-5}$ \\ - Input matrix size & $N_{x} \times N_{y} \times N_{z}$ = From 40$^{3}$ to 200$^{3}$\\ \hline + Input matrix size & $N_{x} \times N_{y} \times N_{z}$ = From 50$^{3}$ to 190$^{3}$\\ \hline \end{tabular} \caption{Test conditions: Input matrix size impacts} \label{tab:05} @@ -739,20 +739,15 @@ of $40\%$ which is only around $24\%$ for the classical GMRES. \label{fig:05} \end{figure} -In these experiments, the input matrix size has been set from $N_{x} = N_{y} -= N_{z} = 40$ to $200$ side elements that is from $40^{3} = 64.000$ to $200^{3} -= 8,000,000$ points. Obviously, as shown in Figure~\ref{fig:05}, the execution -time for both algorithms increases when the input matrix size also increases. -But the interesting results are: -\begin{enumerate} - \item the important increase ($10$ times) of the number of iterations needed to - reach the convergence for the classical GMRES algorithm particularly, when the matrix size - go beyond $N_{x}=150$; \RC{C'est toujours pas clair... ok le nommbre d'itérations est 10 fois plus long mais la suite de la phrase ne veut rien dire} - \RCE{Le nombre d'iterations augmente de 10 fois, cela surtout a partir de N=150} - -\item the classical GMRES execution time is almost the double for $N_{x}=140$ - compared with the Krylov multisplitting method. -\end{enumerate} +In these experiments, the input matrix size has been set from $50^3$ to +$190^3$. Obviously, as shown in Figure~\ref{fig:05}, the execution time for both +algorithms increases when the input matrix size also increases. For all problem +sizes, GMRES is always slower than the Krylov multisplitting. Moreover, for this +benchmark, it seems that the greater the problem size is, the bigger the ratio +between both algorithm execution times is. We can also observ that for some +problem sizes, the Krylov multisplitting convergence varies quite a +lot. Consequently the execution times in that cases also varies. + These findings may help a lot end users to setup the best and the optimal targeted environment for the application deployment when focusing on the problem -- 2.39.5