\end{equation*}
where $\MI$ is the maximum number of outer iterations and $\epsilon$ is the tolerance threshold of the error computed between two successive local solution $X_l^k$ and $X_l^{k+1}$.
-\LZK{Description du processus d'adaptation de l'algo multisplitting à SimGrid}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-We did not encounter major blocking problems when adapting the multisplitting
-algorithm previously described to a simulation environment like SimGrid unless
-some code debugging. Indeed, apart from the review of the program sequence for
-asynchronous exchanges between the six neighbors of each point in a submatrix
-within a cluster or between clusters, the algorithm was executed successfully
-with SMPI and provided identical outputs as those obtained with direct execution
-under MPI. In synchronous mode, the execution of the program raised no
-particular issue but in asynchronous mode, the review of the sequence of
-MPI\_Isend, MPI\_Irecv and MPI\_Waitall instructions and with the addition of
-the primitive MPI\_Test was needed to avoid a memory fault due to an infinite
-loop resulting from the non-convergence of the algorithm. Note here that the use
-of SMPI functions optimizer for memory footprint and CPU usage is not
-recommended knowing that one wants to get real results by simulation. As
-mentioned, upon this adaptation, the algorithm is executed as in the real life
-in the simulated environment after the following minor changes. First, all
-declared global variables have been moved to local variables for each
-subroutine. In fact, global variables generate side effects arising from the
-concurrent access of shared memory used by threads simulating each computing
-units in the SimGrid architecture. Second, the alignment of certain types of
-variables such as ``long int'' had also to be reviewed. Finally, some
-compilation errors on MPI\_Waitall and MPI\_Finalize primitives have been fixed
-with the latest version of SimGrid. In total, the initial MPI program running
-on the simulation environment SMPI gave after a very simple adaptation the same
-results as those obtained in a real environment. We have tested in synchronous
-mode with a simulated platform starting from a modest 2 or 3 clusters grid to a
-larger configuration like simulating Grid5000 with more than 1500 hosts with
-5000 cores~\cite{bolze2006grid}. Once the code debugging and adaptation were
-complete, the next section shows our methodology and experimental results.
+We did not encounter major blocking problems when adapting the multisplitting algorithm previously described to a simulation environment like SIMGRI\LZK[]{SimGrid} unless some code
+debugging. Indeed, apart from the review of the program sequence for asynchronous exchanges between the six neighbors of each point in a submatrix within a cluster or
+between clusters, \LZK{Il faut expliquer pourquoi 6 points voisins (7-point stencil problem)}
+the algorithm was executed successfully with SMPI and provided identical outputs as those obtained with direct execution under MPI. In synchronous
+mode, the execution of the program raised no particular issue but in asynchronous mode, the review of the sequence of MPI\_Isend, MPI\_Irecv and MPI\_Waitall instructions
+and with the addition of the primitive MPI\_Test was needed to avoid a memory fault due to an infinite loop resulting from the non-convergence of the algorithm.
+\LZK{Peut-être mettre plus de précisions sur les difficultés rencontrées dans la version async et les adaptaions effectuées pour SimGrid}
+Note here that the use of SMPI functions optimizer for memory footprint and CPU usage is not recommended knowing that one wants to get real results by simulation.
+As mentioned, upon this adaptation, the algorithm is executed as in the real life in the simulated environment after the following minor changes. First, all declared
+global variables have been moved to local variables for each subroutine. In fact, global variables generate side effects arising from the concurrent access of
+shared memory used by threads simulating each computing unit in the SimGrid architecture. Second, the alignment of certain types of variables such as ``long int'' had
+also to be reviewed. Finally, some compilation errors on MPI\_Waitall and MPI\_Finalize primitives have been fixed with the latest version of SimGrid.
+In total, the initial MPI program running on the simulation environment SMPI gave after a very simple adaptation the same results as those obtained in a real
+environment. We have tested in synchronous mode with a simulated platform starting from a modest 2 or 3 clusters grid to a larger configuration like simulating
+Grid5000 with more than 1500 hosts with 5000 cores~\cite{bolze2006grid}. Once the code debugging and adaptation were complete, the next section shows our methodology and experimental results.\LZK{Dernière phrase peut être supprimée}
+
\section{Experimental results}
-When the \emph{real} application runs in the simulation environment and produces the expected results, varying the input
+When the \textit{real} application runs in the simulation environment and produces the expected results, varying the input
parameters and the program arguments allows us to compare outputs from the code execution. We have noticed from this
study that the results depend on the following parameters:
\begin{itemize}
\item Hosts power (GFlops) can also influence on the results.
\item Finally, when submitting job batches for execution, the arguments values
passed to the program like the maximum number of iterations or the
- \emph{external} precision are critical. They allow to ensure not only the
+ \textit{external} precision are critical. They allow to ensure not only the
convergence of the algorithm but also to get the main objective of the
experimentation of the simulation in having an execution time in asynchronous
less than in synchronous mode (i.e. speed-up less than 1).
\end{itemize}
+\LZK{Propositions pour changer le terme ``speedup'': acceleration ratio ou relative gain}
A priori, obtaining a speedup less than 1 would be difficult in a local area
network configuration where the synchronous mode will take advantage on the
rapid exchange of information on such high-speed links. Thus, the methodology
adopted was to launch the application on clustered network. In this last
configuration, degrading the inter-cluster network performance will
-\emph{penalize} the synchronous mode allowing to get a speedup lower than 1.
+\textit{penalize} the synchronous mode allowing to get a speedup lower than 1.
This action simulates the case of clusters linked with long distance network
like Internet.
matrix size ranging from $N_x = N_y = N_z = \text{62}$ to 171 elements or from
$\text{62}^\text{3} = \text{\np{238328}}$ to $\text{171}^\text{3} =
\text{\np{5211000}}$ entries.
+\LZK{Donner le type et la description du problème traité (problème symétrique Poisson 3D) et préciser peut être aussi qu'on a utilisé un partitionnement 3D}
% use the same column width for the following three tables
\newlength{\mytablew}\settowidth{\mytablew}{\footnotesize\np{E-11}}
\item Maximum number of internal and external iterations;
\item Internal and external precisions;
\item Matrix size $N_x$, $N_y$ and $N_z$;
- \item Matrix diagonal value: \np{6.0};
+ \item Matrix diagonal value: \np{6.0}, \LZK{Off-diagonal values? (-1?)}
\item Execution Mode: synchronous or asynchronous.
\end{itemize}
obtained with a bandwidth of \np[Mbit/s]{1} as shown in
Table~\ref{tab.cluster.3x67}.
+\LZK{Dans le papier, on compare les deux versions synchrone et asycnhrone du multisplitting. Y a t il des résultats pour comparer gmres parallèle classique avec multisplitting asynchrone? Ca permettra de montrer l'intérêt du multisplitting asynchrone sur des clusters distants}
+
\section{Conclusion}
The experimental results on executing a parallel iterative algorithm in
asynchronous mode on an environment simulating a large scale of virtual
This work is partially funded by the Labex ACTION program (contract ANR-11-LABX-01-01).
\todo[inline]{The authors would like to thank\dots{}}
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