\end{figure}
\subsubsection{CPU power impacts on performances\\}
-Using the SimGrid simulator flexibility, we have tried to determine the impact of the CPU power of the processors in the different clusters on performances of both algorithms. We have varied the CPU power from $1$GFlops to $19$GFlops. The simulation is conducted in a grid of 2$\times$16 processors interconnected by the network $N2$ (see Table~\ref{tab:01}) to solve a 3D Poisson problem of size $150^3$. The results depicted in Figure~\ref{fig:06} confirm the performance gain, about $95\%$ for both algorithms, after improving the CPU power of processors.
+
+Using the SimGrid simulator flexibility, we have tried to determine the impact
+of the CPU power of the processors in the different clusters on performances of
+both algorithms. We have varied the CPU power from $1$GFlops to $19$GFlops. The
+simulation is conducted on a grid of $2\times16$ processors interconnected by
+the network $N2$ (see Table~\ref{tab:01}) to solve a 3D Poisson problem of size
+$150^3$. The results depicted in Figure~\ref{fig:06} confirm the performance
+gain, about $95\%$ for both algorithms, after improving the CPU power of
+processors.
\begin{figure}[ht]
\centering
\label{fig:06}
\end{figure}
\ \\
+
To conclude these series of experiments, with SimGrid we have been able to make
many simulations with many parameters variations. Doing all these experiments
-with a real platform is most of the time not possible. Moreover the behavior of
-both GMRES and Krylov two-stage algorithms is in accordance with larger real
-executions on large scale supercomputers~\cite{couturier15}.
+with a real platform is most of the time not possible or very costly. Moreover
+the behavior of both GMRES and Krylov two-stage algorithms is in accordance
+with larger real executions on large scale supercomputers~\cite{couturier15}.
\subsection{Comparison between synchronous GMRES and asynchronous two-stage multisplitting algorithms}
The interest of using an asynchronous algorithm is that there is no more
synchronization. With geographically distant clusters, this may be essential.
-In this case, each processor can compute its iteration freely without any
+In this case, each processor can compute its iterations freely without any
synchronization with the other processors. Thus, the asynchronous may
theoretically reduce the overall execution time and can improve the algorithm
performance.
two-stage algorithm in asynchronous mode with GMRES in synchronous mode. Several
benchmarks have been performed with various combinations of the grid resources
(CPU, Network, matrix size, \ldots). The test conditions are summarized
-in Table~\ref{tab:02}. In order to compare the execution times, Table~\ref{tab:03}
-reports the relative gain between both algorithms. It is defined by the ratio
+in Table~\ref{tab:02}. In order to compare the execution times. Table~\ref{tab:03}
+reports the relative gains between both algorithms. It is defined by the ratio
between the execution time of GMRES and the execution time of the
multisplitting.
\LZK{Quelle table repporte les gains relatifs?? Sûrement pas Table II !!}
Grid architecture & 2$\times$50 totaling 100 processors\\
Processors Power & 1 GFlops to 1.5 GFlops \\
\multirow{2}{*}{Network inter-clusters} & $bw$=1.25 Gbits, $lat=50\mu$s \\
- & $bw$=5 Mbits, $lat=20ms$s\\
+ & $bw$=5 Mbits, $lat=20ms$\\
Matrix size & from $62^3$ to $150^3$\\
Residual error precision & $10^{-5}$ to $10^{-9}$\\ \hline \\
\end{tabular}
