Email:~\email{l.zianekhodja@ulg.ac.be}
}
- \begin{abstract} The behavior of multi-core applications is always a challenge
+ \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
accurate performance models. That is why another solution is to use a simulation
bandwidth, latency, number of processors) and to simulate the execution of such
applications. The main contribution of this paper is to show that the use of a
simulation tool (here we have decided to use the SimGrid toolkit) can really
- help developpers to better tune their applications for a given multi-core
+ help developers to better tune their applications for a given multi-core
architecture.
- In particular we focus our attention on two parallel iterative algorithms based
- on the Multisplitting algorithm and we compare them to the GMRES algorithm.
- These algorithms are used to solve linear systems. Two different variants of
- the Multisplitting are studied: one using synchronoous iterations and another
- one with asynchronous iterations. For each algorithm we have simulated
+ %In particular we focus our attention on two parallel iterative algorithms based
+ %on the Multisplitting algorithm and we compare them to the GMRES algorithm.
+ %These algorithms are used to solve linear systems. Two different variants of
+ %the Multisplitting are studied: one using synchronoous iterations and another
+ %one with asynchronous iterations.
+ In this paper we focus our attention on the simulation of iterative algorithms to solve sparse linear systems on large clusters. We study the behavior of the widely used GMRES algorithm and two different variants of the Multisplitting algorithms: one using synchronous iterations and another one with asynchronous iterations.
+ For each algorithm we have simulated
different architecture parameters to evaluate their influence on the overall
- execution time. The obtain simulated results confirm the real results
- previously obtained on different real multi-core architectures and also confirm
- the efficiency of the asynchronous multisplitting algorithm compared to the
- synchronous GMRES method.
+ execution time.
+ %The obtain simulated results confirm the real results
+ %previously obtained on different real multi-core architectures and also confirm
+ %the efficiency of the asynchronous Multisplitting algorithm compared to the
+ %synchronous GMRES method.
+ The simulations confirm the real results previously obtained on different real multi-core architectures and also confirm the efficiency of the asynchronous Multisplitting algorithm on distant clusters compared to the synchronous GMRES algorithm.
\end{abstract}
parameters as the CPU power, the network parameters (bandwidth and latency)
and with different problem size. The relative gains greater than $1$ between the
two algorithms have been captured after each step of the test. In
- Figure~\ref{fig:07} are reported the best grid configurations allowing
+ Table~\ref{tab:08} are reported the best grid configurations allowing
the multisplitting method to be more than $2.5$ times faster than the
classical GMRES. These experiments also show the relative tolerance of the
multisplitting algorithm when using a low speed network as usually observed with
\end{tabular}}
- \begin{figure}[!t]
+ \begin{table}[!t]
\centering
%\begin{table}
% \caption{Relative gain of the multisplitting algorithm compared with the classical GMRES}
\hline
\end{mytable}
%\end{table}
- \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}
+ \caption{Relative gain of the multisplitting algorithm compared with the classical GMRES}
+ \label{tab:08}
+ \end{table}
\section{Conclusion}
-CONCLUSION
+
+In this paper we have presented the simulation of the execution of three
+different parallel solvers on some multi-core architectures. We have show that
+the SimGrid toolkit is an interesting simulation tool that has allowed us to
+determine which method to choose given a specified multi-core architecture.
+Moreover the simulated results are in accordance (i.e. with the same order of
+magnitude) with the works presented in~\cite{couturier15}. Simulated results
+also confirm the efficiency of the asynchronous multisplitting
+algorithm compared to the synchronous GMRES especially in case of
+geographically distant clusters.
+
+These results are important since it is very time consuming to find optimal
+configuration and deployment requirements for a given application on a given
+multi-core architecture. Finding good resource allocations policies under
+varying CPU power, network speeds and loads is very challenging and labor
+intensive. This problematic is even more difficult for the asynchronous
+scheme where a small parameter variation of the execution platform and of the
+application data can lead to very different numbers of iterations to reach the
+converge and so to very different execution times.
+
+
+Our future works...
+
%\section*{Acknowledgment}
