%% execution time.
%% 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.
-
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 tool which allows us to change many parameters of the architecture (network bandwidth, latency, number of processors) and to simulate the execution of such applications.
-In this paper we focus on the simulation of iterative algorithms to solve sparse linear systems. We study the behavior of the GMRES algorithm and two different variants of the Multisplitting algorithms: using synchronous or asynchronous iterations. For each algorithm we have simulated different architecture parameters to evaluate their influence on the overall execution time. 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 GMRES algorithm.
+In this paper we focus on the simulation of iterative algorithms to solve sparse linear systems. We study the behavior of the GMRES algorithm and two different variants of the multisplitting algorithms: using synchronous or asynchronous iterations. For each algorithm we have simulated different architecture parameters to evaluate their influence on the overall execution time. 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 GMRES algorithm.
+
\end{abstract}
%\keywords{Algorithm; distributed; iterative; asynchronous; simulation; simgrid;
from its neighbors. We say that the iteration computation follows a
\textit{synchronous} scheme. In the asynchronous scheme a task can compute a new
iteration without having to wait for the data dependencies coming from its
-neighbors. Both communication and computations are \textit{asynchronous}
+neighbors. Both communications and computations are \textit{asynchronous}
inducing that there is no more idle time, due to synchronizations, between two
iterations~\cite{bcvc06:ij}. This model presents some advantages and drawbacks
-that we detail in section~\ref{sec:asynchro} but even if the number of
+that we detail in Section~\ref{sec:asynchro} but even if the number of
iterations required to converge is generally greater than for the synchronous
case, it appears that the asynchronous iterative scheme can significantly
reduce overall execution times by suppressing idle times due to
challenging and labor intensive~\cite{Calheiros:2011:CTM:1951445.1951450}. 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
+lead to very different numbers of iterations to reach the convergence and so to
very different execution times. In this challenging context we think that the
use of a simulation tool can greatly leverage the possibility of testing various
platform scenarios.
The {\bf main contribution of this paper} is to show that the use of a
simulation tool (i.e. the SimGrid toolkit~\cite{SimGrid}) in the context of real
parallel applications (i.e. large linear system solvers) can help developers to
-better tune their application for a given multi-core architecture. To show the
+better tune their applications for a given multi-core architecture. To show the
validity of this approach we first compare the simulated execution of the Krylov
-multisplitting algorithm with the GMRES (Generalized Minimal Residual)
+multisplitting algorithm with the GMRES (Generalized Minimal RESidual)
solver~\cite{saad86} in synchronous mode. The simulation results allow us to
-determine which method to choose given a specified multi-core architecture.
+determine which method to choose for a given multi-core architecture.
Moreover the obtained results on different simulated multi-core architectures
confirm the real results previously obtained on non simulated architectures.
More precisely the simulated results are in accordance (i.e. with the same order
of magnitude) with the works presented in~\cite{couturier15}, which show that
-the synchronous multisplitting method is more efficient than GMRES for large
+the synchronous Krylov multisplitting method is more efficient than GMRES for large
scale clusters. Simulated results also confirm the efficiency of the
asynchronous multisplitting algorithm compared to the synchronous GMRES
especially in case of geographically distant clusters.
This paper is organized as follows. Section~\ref{sec:asynchro} presents the
iteration model we use and more particularly the asynchronous scheme. In
-section~\ref{sec:simgrid} the SimGrid simulation toolkit is presented.
+Section~\ref{sec:simgrid} the SimGrid simulation toolkit is presented.
Section~\ref{sec:04} details the different solvers that we use. Finally our
-experimental results are presented in section~\ref{sec:expe} followed by some
+experimental results are presented in Section~\ref{sec:expe} followed by some
concluding remarks and perspectives.
