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}.
-
+environment. We have successfully executed the code in synchronous mode using GMRES algorithm compared with a multisplitting method in asynchrnous mode after few modification.
\section{Experimental results}
\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).
+ less than in synchronous mode. The ratio between the execution time of asynchronous compared to the synchronous mode is defined as the "relative gain". So, our objective running the algorithm in SimGrid is to obtain a relative gain greater than 1.
\end{itemize}
\LZK{Propositions pour remplacer le terme ``speedup'': acceleration ratio ou relative gain}
-
-A priori, obtaining a speedup less than 1 would be difficult in a local area
+\CER{C'est fait. En conséquence, les tableaux et les commentaires ont été aussi modifiés}
+A priori, obtaining a relative gain greater 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
-\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
+\textit{penalize} the synchronous mode allowing to get a relative gain greater than 1.
+This action simulates the case of distant clusters linked with long distance network
like Internet.
In this paper, we solve the 3D Poisson problem whose the mathematical model is
Prec/Eprec
& \np{E-5} & \np{E-8} & \np{E-9} & \np{E-11} & \np{E-11} & \np{E-11} \\
\hline
- speedup
- & 0.396 & 0.392 & 0.396 & 0.391 & 0.393 & 0.395 \\
+ Relative gain
+ & 2.52 & 2.55 & 2.52 & 2.57 & 2.54 & 2.53 \\
\hline
\end{mytable}
Prec/Eprec
& \np{E-11} & \np{E-11} & \np{E-11} & \np{E-11} & \np{E-5} & \np{E-5} \\
\hline
- speedup
- & 0.398 & 0.388 & 0.393 & 0.394 & 0.63 & 0.778 \\
+ Relative gain
+ & 2.51 & 2.58 & 2.55 & 2.54 & 1.59 & 1.29 \\
\hline
\end{mytable}
\end{table}
respectively 33, 33 and 34 hosts, or again by on hundred hosts for all the
clusters. In the same way as above, a judicious choice of key parameters has
permitted to get the results in Table~\ref{tab.cluster.3x33} which shows the
-speedups less than 1 with a matrix size from 62 to 100 elements.
+relative gains greater than 1 with a matrix size from 62 to 100 elements.
\begin{table}[!t]
\centering
Prec/Eprec
& \np{E-5} & \np{E-5} & \np{E-5} & \np{E-5} & \np{E-5} & \np{E-5} \\
\hline
- speedup
- & 0.997 & 0.99 & 0.93 & 0.84 & 0.78 & 0.99 \\
+ Relative gain
+ & 1.003 & 1,01 & 1,08 & 0.19 & 1.28 & 1.01 \\
\hline
\end{mytable}
\end{table}
\hline
Prec/Eprec & \np{E-5} \\
\hline
- speedup & 0.9 \\
+ Relative gain & 1.11 \\
\hline
\end{mytable}
\end{table}
After analyzing the outputs, generally, for the configuration with two or three
clusters including one hundred hosts (Tables~\ref{tab.cluster.2x50}
and~\ref{tab.cluster.3x33}), some combinations of the used parameters affecting
-the results have given a speedup less than 1, showing the effectiveness of the
+the results have given a relative gain more than 2.5, showing the effectiveness of the
asynchronous performance compared to the synchronous mode.
In the case of a two clusters configuration, Table~\ref{tab.cluster.2x50} shows
of one GFlops, an efficiency of about \np[\%]{40} in asynchronous mode is
obtained for a matrix size of 62 elements. It is noticed that the result remains
stable even if we vary the external precision from \np{E-5} to \np{E-9}. By
-increasing the problem size up to 100 elements, it was necessary to increase the
+increasing the matrix size up to 100 elements, it was necessary to increase the
CPU power of \np[\%]{50} to \np[GFlops]{1.5} for a convergence of the algorithm
with the same order of asynchronous mode efficiency. Maintaining such a system
power but this time, increasing network throughput inter cluster up to
-\np[Mbit/s]{50}, the result of efficiency of about \np[\%]{40} is obtained with
+\np[Mbit/s]{50}, the result of efficiency with a relative gain of 1.5 is obtained with
high external precision of \np{E-11} for a matrix size from 110 to 150 side
elements.
For the 3 clusters architecture including a total of 100 hosts,
Table~\ref{tab.cluster.3x33} shows that it was difficult to have a combination
-which gives an efficiency of asynchronous below \np[\%]{80}. Indeed, for a
+which gives a relative gain of asynchronous mode more than 1.2. Indeed, for a
matrix size of 62 elements, equality between the performance of the two modes
(synchronous and asynchronous) is achieved with an inter cluster of
-\np[Mbit/s]{10} and a latency of \np[ms]{E-1}. To challenge an efficiency by
-\np[\%]{78} with a matrix size of 100 points, it was necessary to degrade the
+\np[Mbit/s]{10} and a latency of \np[ms]{E-1}. To challenge an efficiency greater than 1.2 with a matrix size of 100 points, it was necessary to degrade the
inter cluster network bandwidth from 5 to \np[Mbit/s]{2}.
A last attempt was made for a configuration of three clusters but more powerful
-with 200 nodes in total. The convergence with a speedup of \np[\%]{90} was
+with 200 nodes in total. The convergence with a relative gain around 1.1 was
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}
+\CER{En fait, les résultats ont été obtenus en comparant les temps d'exécution entre l'algo classique GMRES en mode synchrone avec le multisplitting en mode asynchrone, le tout sur un environnement de clusters distants}
\section{Conclusion}
The experimental results on executing a parallel iterative algorithm in
