concluding remarks and perspectives.
-\section{The asynchronous iteration model}
+\section{The asynchronous iteration model and the motivations of our work}
\label{sec:asynchro}
Asynchronous iterative methods have been studied for many years theoritecally and
it must not synchronize all the processors. Interested readers can
consult~\cite{myBCCV05c,bahi07,ccl09:ij}.
+The number of iterations required to reach the convergence is generally greater
+for the asynchronous scheme (this number depends depends on the delay of the
+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
+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
+architecture are often very important. So, prior to delpoyment and tests it
+seems very promising to be able to simulate the behavior of asynchronous
+iterative algorithms. The problematic is then to show that the results produce
+by simulation are in accordance with reality i.e. of the same order of
+magnitude. To our knowledge, there is no study on this problematic.
+
\section{SimGrid}
\label{sec:simgrid}
in the grid: in average, the GMRES (resp. Multisplitting) algorithm performs
$40\%$ better (resp. $48\%$) when running from 2x16=32 to 8x8=64 processors.
-\subsubsection{Running on two different inter-clusters network speeds \\}
+\subsubsection{Running on two different inter-clusters network speeds \\}
\begin{table} [ht!]
\begin{center}
Figure~\ref{fig:02} shows that end users will gain to reduce the execution time
for both algorithms in using a grid architecture like 4x16 or 8x8: the
performance was increased by a factor of $2$. The results depict also that when
-the network speed drops down (variation of 12.5\%), the difference between the two Multisplitting algorithms execution times can reach more than 25\%.
+the network speed drops down (variation of 12.5\%), the difference between the two Multisplitting algorithms execution times can reach more than 25\%.
%\RC{c'est pas clair : la différence entre quoi et quoi?}
%\DL{pas clair}
%\RCE{Modifie}
