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.
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
\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}}
