X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/rce2015.git/blobdiff_plain/c6459f3420747227cfe477c0e22f08499ee3e4de..7c8fb94ad3ce704f81876b1dade93846a931a5a8:/paper.tex?ds=inline diff --git a/paper.tex b/paper.tex index 0dc584b..46ecc39 100644 --- a/paper.tex +++ b/paper.tex @@ -346,19 +346,18 @@ nodes/processors for each cluster). In addition, the following arguments are given to the programs at runtime: \begin{itemize} - \item maximum number of inner and outer iterations; - \item inner and outer precisions; - \item maximum number of the GMRES restarts in the Arnorldi process; - \item maximum number of iterations and the tolerance threshold in classical GMRES; - \item tolerance threshold for outer and inner-iterations; - \item matrix size (N$_{x}$, N$_{y}$ and N$_{z}$) respectively on $x, y, z$ axis; - \item matrix diagonal value is fixed to $6.0$ for synchronous Krylov multisplitting experiments and $6.2$ for asynchronous block Jacobi experiments; \RC{CE tu vérifies, je dis ca de tête} - \item matrix off-diagonal value; - \item execution mode: synchronous or asynchronous; - \RCE {C'est ok la liste des arguments du programme mais si Lilia ou toi pouvez preciser pour les arguments pour CGLS ci dessous} \RC{Vu que tu n'as pas fait varier ce paramètre, on peut ne pas en parler} - \item Size of matrix S; - \item Maximum number of iterations and tolerance threshold for CGLS. + \item maximum number of inner iterations $\MIG$ and outer iterations $\MIM$, + \item inner precision $\TOLG$ and outer precision $\TOLM$, + \item matrix sizes of the 3D Poisson problem: N$_{x}$, N$_{y}$ and N$_{z}$ on axis $x$, $y$ and $z$ respectively, + \item matrix diagonal value is fixed to $6.0$ for synchronous Krylov multisplitting experiments and $6.2$ for asynchronous block Jacobi experiments, + \item matrix off-diagonal value is fixed to $-1.0$, + \item number of vectors in matrix $S$ (i.e. value of $s$), + \item maximum number of iterations $\MIC$ and precision $\TOLC$ for CGLS method, + \item maximum number of iterations and precision for the classical GMRES method, + \item maximum number of restarts for the Arnorldi process in GMRES method, + \item execution mode: synchronous or asynchronous. \end{itemize} +\LZK{CE pourrais tu vérifier et confirmer les valeurs des éléments diag et off-diag de la matrice?} It should also be noticed that both solvers have been executed with the Simgrid selector \texttt{-cfg=smpi/running\_power} which determines the computational power (here 19GFlops) of the simulator host machine. @@ -716,7 +715,7 @@ get the highest \textit{"relative gain"} (exec\_time$_{GMRES}$ / exec\_time$_{multisplitting}$) in comparison with the classical GMRES time. -The test conditions are summarized in the table below : \\ +The test conditions are summarized in the table below: \\ \begin{figure} [ht!] \centering @@ -732,14 +731,14 @@ The test conditions are summarized in the table below : \\ \end{figure} Again, comprehensive and extensive tests have been conducted with different -parametes as the CPU power, the network parameters (bandwidth and latency) in -the simulator tool and with different problem size. The relative gains greater -than 1 between the two algorithms have been captured after each step of the -test. In Figure~\ref{table:01} are reported the best grid configurations -allowing the multisplitting method to be more than 2.5 times faster than the +parameters as the CPU power, the network parameters (bandwidth and latency) +and with different problem size. The relative gains greater than $1$ between the +two algorithms have been captured after each step of the test. In +Figure~\ref{table:01} are reported the best grid configurations allowing +the multisplitting method to be more than $2.5$ times faster than the classical GMRES. These experiments also show the relative tolerance of the multisplitting algorithm when using a low speed network as usually observed with -geographically distant clusters throuth the internet. +geographically distant clusters through the internet. % use the same column width for the following three tables \newlength{\mytablew}\settowidth{\mytablew}{\footnotesize\np{E-11}}