\todo[color=blue!10,#1]{\sffamily\textbf{LZK:} #2}\xspace}
\newcommand{\RC}[2][inline]{%
\todo[color=red!10,#1]{\sffamily\textbf{RC:} #2}\xspace}
+\newcommand{\CER}[2][inline]{%
+ \todo[color=pink!10,#1]{\sffamily\textbf{CER:} #2}\xspace}
\algnewcommand\algorithmicinput{\textbf{Input:}}
\algnewcommand\Input{\item[\algorithmicinput]}
asynchronous mode algorithms by comparing their performance with the synchronous
mode. More precisely, we had implemented a program for solving large
non-symmetric linear system of equations by numerical method GMRES (Generalized
-Minimal Residual) []\AG[]{[]?}. We show, that with minor modifications of the
+Minimal Residual) []\AG[]{[]?}.\LZK{Problème traité dans le papier est symétrique ou asymétrique? (Poisson 3D symétrique?)} We show, that with minor modifications of the
initial MPI code, the SimGrid toolkit allows us to perform a test campaign of a
real AIAC application on different computing architectures. The simulated
results we obtained are in line with real results exposed in ??\AG[]{??}.
Sequential Processes, SimDAG to simulate DAGs of (parallel) tasks, and SMPI to
run real applications written in MPI~\cite{MPI}. Apart from the native C
interface, SimGrid provides bindings for the C++, Java, Lua and Ruby programming
-languages. The SMPI interface supports applications written in C or Fortran,
-with little or no modifications. SMPI implements about \np[\%]{80} of the MPI
-2.0 standard~\cite{bedaride:hal-00919507}.
-
-%%% explain simulation
-%- simulated processes folded in one real process
-%- simulates interactions on the network, fluid model
-%- able to skip long-lasting computations
-%- traces + visu?
-
-%%% platforms
-%- describe resources and their interconnection, with their properties
-%- XML files
-
-%%% validation + refs
+languages. SMPI is the interface that has been used for the work exposed in
+this paper. The SMPI interface implements about \np[\%]{80} of the MPI 2.0
+standard~\cite{bedaride:hal-00919507}, and supports applications written in C or
+Fortran, with little or no modifications.
+
+With SimGrid, the execution of a distributed application is simulated on a
+single machine. The application code is really executed, but some operations
+like the communications are intercepted to be simulated according to the
+characteristics of the simulated execution platform. The description of this
+target platform is given as an input for the execution, by the mean of an XML
+file. It describes the properties of the platform, such as the computing node
+with their computing power, the interconnection links with their bandwidth and
+latency, and the routing strategy. The simulated running time of the
+application is computed according to these properties.
+
+\AG{Faut-il ajouter quelque-chose ?}
+\CER{Comme tu as décrit la plateforme d'exécution, on peut ajouter éventuellement le fichier XML contenant des hosts dans les clusters formant la grille}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Simulation of the multisplitting method}
\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 SimGrid unless some code
+debugging. Indeed, apart from the review of the program sequence for asynchronous exchanges between the six neighbors of each point (left,right,front,behind,top,down) in a cubic partitionned submatrix within a cluster or between clusters, \CER{J'ai rajouté quelques précisions mais serait-il nécessaire de décrire a ce niveau la discrétisation 3D ?}
+\LZK{Non ce n'est pas nécessaire. A ce niveau, on décrit l'algorithme général de multisplitting. Donc, je pense qu'il est préférable de ne pas préciser le schéma de communication qui peut changer selon le type de problème. \\ {\bf Par exemple: Indeed, apart from the review of the program sequence for asynchronous exchanges between processors 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.
+\CER{On voulait en fait montrer la simplicité de l'adaptation de l'algo a SimGrid. Les problèmes rencontrés décrits dans ce paragraphe concerne surtout le mode async}\LZK{OK. J'aurais préféré avoir un peu plus de détails sur l'adaptation de la version async}
+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}.
+
\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.
-
+\CER{Voir ma remarque plus si nécessaire de décrire en détail le partitionnement 3D}
+\LZK{Je pense qu'il faut donner ici le type du problème traité (Poisson 3D). Le partitionnement 3D permet juste de définir le schéma de dépendances (1 proc a au max 6 voisins dans le cluster local ou dans les clusters distants)}
% use the same column width for the following three tables
\newlength{\mytablew}\settowidth{\mytablew}{\footnotesize\np{E-11}}
\newenvironment{mytable}[1]{% #1: number of columns for data
\item Maximum number of internal and external iterations;
\item Internal and external precisions;
\item Matrix size $N_x$, $N_y$ and $N_z$;
+%<<<<<<< HEAD
\item Matrix diagonal value: \np{6.0};
+ \item Matrix Off-diagonal value: \np{-1.0};
+%=======
+%>>>>>>> 5fb6769d88c1720b6480a28521119ef010462fa6
\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
tool to run efficiently an iterative parallel algorithm in asynchronous
mode in a grid architecture.
+\LZK{Perspectives???}
+
\section*{Acknowledgment}
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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+
+
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