\section{Motivations and scientific context}
-As exposed in the introduction, parallel iterative methods are now widely used in many scientific domains. They can be
-classified in three main classes depending on how iterations and communications are managed (for more details readers
-can refer to~\cite{bcvc06:ij}). In the \textit{Synchronous Iterations~-- Synchronous Communications (SISC)} model data
-are exchanged at the end of each iteration. All the processors must begin the same iteration at the same time and
-important idle times on processors are generated. The \textit{Synchronous Iterations~-- Asynchronous Communications
-(SIAC)} model can be compared to the previous one except that data required on another processor are sent asynchronously
-i.e. without stopping current computations. This technique allows to partially overlap communications by computations
-but unfortunately, the overlapping is only partial and important idle times remain. It is clear that, in a grid
-computing context, where the number of computational nodes is large, heterogeneous and widely distributed, the idle
-times generated by synchronizations are very penalizing. One way to overcome this problem is to use the
-\textit{Asynchronous Iterations~-- Asynchronous Communications (AIAC)} model. Here, local computations do not need to
-wait for required data. Processors can then perform their iterations with the data present at that time. Figure~\ref{fig:aiac}
-illustrates this model where the gray blocks represent the computation phases, the white spaces the idle
-times and the arrows the communications.
-\AG{There are no ``white spaces'' on the figure.}
-With this algorithmic model, the number of iterations required before the
-convergence is generally greater than for the two former classes. But, and as detailed in~\cite{bcvc06:ij}, AIAC
-algorithms can significantly reduce overall execution times by suppressing idle times due to synchronizations especially
-in a grid computing context.\LZK{Répétition par rapport à l'intro}
+As exposed in the introduction, parallel iterative methods are now widely used
+in many scientific domains. They can be classified in three main classes
+depending on how iterations and communications are managed (for more details
+readers can refer to~\cite{bcvc06:ij}). In the \textit{Synchronous Iterations~--
+ Synchronous Communications (SISC)} model data are exchanged at the end of each
+iteration. All the processors must begin the same iteration at the same time and
+important idle times on processors are generated. The \textit{Synchronous
+ Iterations~-- Asynchronous Communications (SIAC)} model can be compared to the
+previous one except that data required on another processor are sent
+asynchronously i.e. without stopping current computations. This technique
+allows to partially overlap communications by computations but unfortunately,
+the overlapping is only partial and important idle times remain. It is clear
+that, in a grid computing context, where the number of computational nodes is
+large, heterogeneous and widely distributed, the idle times generated by
+synchronizations are very penalizing. One way to overcome this problem is to use
+the \textit{Asynchronous Iterations~-- Asynchronous Communications (AIAC)}
+model. Here, local computations do not need to wait for required
+data. Processors can then perform their iterations with the data present at that
+time. Figure~\ref{fig:aiac} illustrates this model where the gray blocks
+represent the computation phases. With this algorithmic model, the number of
+iterations required before the convergence is generally greater than for the two
+former classes. But, and as detailed in~\cite{bcvc06:ij}, AIAC algorithms can
+significantly reduce overall execution times by suppressing idle times due to
+synchronizations especially in a grid computing context.
+%\LZK{Répétition par rapport à l'intro}
\begin{figure}[!t]
\centering
\label{fig:aiac}
\end{figure}
+\RC{Je serais partant de virer AIAC et laisser asynchronous algorithms... à voir}
+
+%% It is very challenging to develop efficient applications for large scale,
+%% heterogeneous and distributed platforms such as computing grids. Researchers and
+%% engineers have to develop techniques for maximizing application performance of
+%% these multi-cluster platforms, by redesigning the applications and/or by using
+%% novel algorithms that can account for the composite and heterogeneous nature of
+%% the platform. Unfortunately, the deployment of such applications on these very
+%% large scale systems is very costly, labor intensive and time consuming. In this
+%% context, it appears that the use of simulation tools to explore various platform
+%% scenarios at will and to run enormous numbers of experiments quickly can be very
+%% promising. Several works\dots{}
+
+%% \AG{Several works\dots{} what?\\
+% Le paragraphe suivant se trouve déjà dans l'intro ?}
+In the context of asynchronous algorithms, the number of iterations to reach the
+convergence depends on the delay of messages. With synchronous iterations, the
+number of iterations is exactly the same than in the sequential mode (if the
+parallelization process does not change the algorithm). So the difficulty with
+asynchronous algorithms comes from the fact it is necessary to run the algorithm
+with real data. In fact, from an execution to another the order of messages will
+change and the number of iterations to reach the convergence will also change.
+According to all the parameters of the platform (number of nodes, power of
+nodes, inter and intra clusrters bandwith and latency, ....) and of the
+algorithm (number of splitting with the multisplitting algorithm), the
+multisplitting code will obtain the solution more or less quickly. Or course,
+the GMRES method also depends of the same parameters. As it is difficult to have
+access to many clusters, grids or supercomputers with many different network
+parameters, it is interesting to be able to simulate the behaviors of
+asynchronous iterative algoritms before being able to runs real experiments.
+
-It is very challenging to develop efficient applications for large scale,
-heterogeneous and distributed platforms such as computing grids. Researchers and
-engineers have to develop techniques for maximizing application performance of
-these multi-cluster platforms, by redesigning the applications and/or by using
-novel algorithms that can account for the composite and heterogeneous nature of
-the platform. Unfortunately, the deployment of such applications on these very
-large scale systems is very costly, labor intensive and time consuming. In this
-context, it appears that the use of simulation tools to explore various platform
-scenarios at will and to run enormous numbers of experiments quickly can be very
-promising. Several works\dots{}
-
-\AG{Several works\dots{} what?\\
- Le paragraphe suivant se trouve déjà dans l'intro ?}
-In the context of AIAC algorithms, the use of simulation tools is even more
-relevant. Indeed, this class of applications is very sensible to the execution
-environment context. For instance, variations in the network bandwidth (intra
-and inter-clusters), in the number and the power of nodes, in the number of
-clusters\dots{} can lead to very different number of iterations and so to very
-different execution times.
