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analysis of simulated grid-enabled numerical iterative algorithms}
%\itshape{\journalnamelc}\footnotemark[2]}
-\author{ Charles Emile Ramamonjisoa and
- David Laiymani and
- Arnaud Giersch and
- Lilia Ziane Khodja and
- Raphaël Couturier
+\author{Charles Emile Ramamonjisoa\affil{1},
+ David Laiymani\affil{1},
+ Arnaud Giersch\affil{1},
+ Lilia Ziane Khodja\affil{2} and
+ Raphaël Couturier\affil{1}
}
\address{
- \centering
- Femto-ST Institute - DISC Department\\
- Université de Franche-Comté\\
- Belfort\\
- Email: \email{{raphael.couturier,arnaud.giersch,david.laiymani,charles.ramamonjisoa}@univ-fcomte.fr}
+ \affilnum{1}%
+ Femto-ST Institute, DISC Department,
+ University of Franche-Comté,
+ Belfort, France.
+ Email:~\email{{charles.ramamonjisoa,david.laiymani,arnaud.giersch,raphael.couturier}@univ-fcomte.fr}\break
+ \affilnum{2}
+ Department of Aerospace \& Mechanical Engineering,
+ Non Linear Computational Mechanics,
+ University of Liege, Liege, Belgium.
+ Email:~\email{l.zianekhodja@ulg.ac.be}
}
-%% Lilia Ziane Khodja: Department of Aerospace \& Mechanical Engineering\\ Non Linear Computational Mechanics\\ University of Liege\\ Liege, Belgium. Email: l.zianekhodja@ulg.ac.be
-
\begin{abstract} The behavior of multi-core applications is always a challenge
to predict, especially with a new architecture for which no experiment has been
performed. With some applications, it is difficult, if not impossible, to build
given application for a given architecture. In this way and in order to reduce
the access cost to these computing resources it seems very interesting to use a
simulation environment. The advantages are numerous: development life cycle,
-code debugging, ability to obtain results quickly~\ldots. In counterpart, the simulation results need to be consistent with the real ones.
+code debugging, ability to obtain results quickly\dots{} In counterpart, the simulation results need to be consistent with the real ones.
In this paper we focus on a class of highly efficient parallel algorithms called
\emph{iterative algorithms}. The parallel scheme of iterative methods is quite
messages). Note that, it is not the case in the synchronous mode where the
number of iterations is the same than in the sequential mode. In this way, the
set of the parameters of the platform (number of nodes, power of nodes,
-inter and intra clusters bandwidth and latency \ldots) and of the
+inter and intra clusters bandwidth and latency, \ldots) and of the
application can drastically change the number of iterations required to get the
convergence. It follows that asynchronous iterative algorithms are difficult to
optimize since the financial and deployment costs on large scale multi-core
Input matrix size & N$_{x}$ x N$_{y}$ x N$_{z}$ =150 x 150 x 150\\ %\hline
- & N$_{x}$ x N$_{y}$ x N$_{z}$ =170 x 170 x 170 \\ \hline
\end{tabular}
-\caption{Test conditions: various grid configurations with the input matix size N$_{x}$=150 or N$_{x}$=170 \RC{N2 n'est pas défini..}\RC{Nx est défini, Ny? Nz?}}
+\caption{Test conditions: various grid configurations with the input matix size N$_{x}$=150 or N$_{x}$=170 \RC{N2 n'est pas défini..}\RC{Nx est défini, Ny? Nz?}
+\AG{La lettre 'x' n'est pas le symbole de la multiplication. Utiliser \texttt{\textbackslash times}. Idem dans le texte, les figures, etc.}}
\label{tab:01}
\end{center}
\end{table}
\begin{center}
\includegraphics[width=100mm]{cluster_x_nodes_nx_150_and_nx_170.pdf}
\end{center}
- \caption{Various grid configurations with the input matrix size N$_{x}$=150 and N$_{x}$=170\RC{idem}}
+ \caption{Various grid configurations with the input matrix size N$_{x}$=150 and N$_{x}$=170\RC{idem}
+\AG{Utiliser le point comme séparateur décimal et non la virgule. Idem dans les autres figures.}}
\label{fig:01}
\end{figure}
\begin{figure} [ht!]
\centering
\includegraphics[width=100mm]{cluster_x_nodes_n1_x_n2.pdf}
-\caption{Grid 2x16 and 4x8 with networks N1 vs N2}
+\caption{Grid 2x16 and 4x8 with networks N1 vs N2
+\AG{\np{8E-6}, \np{5E-6} au lieu de 8E-6, 5E-6}}
\label{fig:02}
\end{figure}
%\end{wrapfigure}
\begin{figure} [ht!]
\centering
\includegraphics[width=100mm]{network_latency_impact_on_execution_time.pdf}
-\caption{Network latency impacts on execution time}
+\caption{Network latency impacts on execution time
+\AG{\np{E-6}}}
\label{fig:03}
\end{figure}
-According to the results of Figure~\ref{fig:03}, a degradation of the network
-latency from $8.10^{-6}$ to $6.10^{-5}$ implies an absolute time increase of more
-than $75\%$ (resp. $82\%$) of the execution for the classical GMRES (resp. Krylov
-multisplitting) algorithm. In addition, it appears that the Krylov
-multisplitting method tolerates more the network latency variation with a less
-rate increase of the execution time. Consequently, in the worst case
-($lat=6.10^{-5 }$), the execution time for GMRES is almost the double than the
-time of the Krylov multisplitting, even though, the performance was on the same
-order of magnitude with a latency of $8.10^{-6}$.
+According to the results of Figure~\ref{fig:03}, a degradation of the network
+latency from $8.10^{-6}$ to $6.10^{-5}$ implies an absolute time increase of
+more than $75\%$ (resp. $82\%$) of the execution for the classical GMRES
+(resp. Krylov multisplitting) algorithm. In addition, it appears that the
+Krylov multisplitting method tolerates more the network latency variation with a
+less rate increase of the execution time.\RC{Les 2 précédentes phrases me
+ semblent en contradiction....} Consequently, in the worst case ($lat=6.10^{-5
+}$), the execution time for GMRES is almost the double than the time of the
+Krylov multisplitting, even though, the performance was on the same order of
+magnitude with a latency of $8.10^{-6}$.
\subsubsection{Network bandwidth impacts on performance}
\ \\
Network & N1 : bw=1Gbs - lat=5.10$^{-5}$ \\ %\hline
Input matrix size & N$_{x}$ x N$_{y}$ x N$_{z}$ =150 x 150 x 150\\ \hline \\
\end{tabular}
-\caption{Test conditions: Network bandwidth impacts}
+\caption{Test conditions: Network bandwidth impacts\RC{Qu'est ce qui varie ici? Il n'y a pas de variation dans le tableau}}
\label{tab:04}
\end{table}
\begin{figure} [ht!]
\centering
\includegraphics[width=100mm]{network_bandwith_impact_on_execution_time.pdf}
-\caption{Network bandwith impacts on execution time}
+\caption{Network bandwith impacts on execution time
+\AG{``Execution time'' avec un 't' minuscule}. Idem autres figures.}
\label{fig:04}
\end{figure}
time for both algorithms increases when the input matrix size also increases.
But the interesting results are:
\begin{enumerate}
- \item the drastic increase ($10$ times) \RC{Je ne vois pas cela sur la figure}
-\RCE{Corrige} of the number of iterations needed to reach the convergence for the classical
-GMRES algorithm when the matrix size go beyond $N_{x}=150$;
+ \item the drastic increase ($10$ times) of the number of iterations needed to
+ reach the convergence for the classical GMRES algorithm when the matrix size
+ go beyond $N_{x}=150$; \RC{C'est toujours pas clair... ok le nommbre d'itérations est 10 fois plus long mais la suite de la phrase ne veut rien dire}
\item the classical GMRES execution time is almost the double for $N_{x}=140$
compared with the Krylov multisplitting method.
\end{enumerate}
\hline
\end{mytable}
%\end{table}
- \caption{Relative gain of the multisplitting algorithm compared with the classical GMRES}
+ \caption{Relative gain of the multisplitting algorithm compared with the classical GMRES
+\AG{C'est un tableau, pas une figure}}
\label{fig:07}
\end{figure}
CONCLUSION
-\section*{Acknowledgment}
-
+%\section*{Acknowledgment}
+\ack
This work is partially funded by the Labex ACTION program (contract ANR-11-LABX-01-01).
-
\bibliographystyle{wileyj}
\bibliography{biblio}
+\AG{Des warnings bibtex à corriger (%
+ \texttt{entry type for "SimGrid" isn't style-file defined},
+ \texttt{empty booktitle in Bru95}%
+).}
\end{document}
