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 \section{The asynchronous iteration model}
 
-\DL{Décrire le modèle asynchrone. Je m'en charge}
+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{bcvc02:ip}). 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 grey blocks represent the computation
+phases, the white spaces the idle times and the arrows the
+communications. 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.
+
+\begin{figure}[htbp]
+  \centering
+    \includegraphics[width=8cm]{AIAC.pdf}
+  \caption{The Asynchronous Iterations - Asynchronous Communications model } 
+  \label{fig:aiac}
+\end{figure}
+
+
+
 
 \section{SimGrid}