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}. 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
solver~\cite{saad86} in synchronous mode. The simulation results allow us to
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.
+confirm the real results previously obtained on real physical 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 Krylov multisplitting method is more efficient than GMRES for large
Asynchronous iterative methods have been studied for many years theoretically and
practically. Many methods have been considered and convergence results have been
proved. These methods can be used to solve, in parallel, fixed point problems
-(i.e. problems for which the solution is $x^\star =f(x^\star)$. In practice,
+(i.e. problems for which the solution is $x^\star =f(x^\star)$). In practice,
asynchronous iteration methods can be used to solve, for example, linear and
non-linear systems of equations or optimization problems, interested readers are
invited to read~\cite{BT89,bahi07}.
algorithm that supports both the synchronous or the asynchronous iteration model
requires very few modifications to be able to be executed in both variants. In
practice, only the communications and convergence detection are different. In
-the synchronous mode, iterations are synchronized whereas in the asynchronous
-one, they are not. It should be noticed that non-blocking communications can be
+the synchronous mode iterations are synchronized, whereas in the asynchronous
+one they are not. It should be noticed that non-blocking communications can be
used in both modes. Concerning the convergence detection, synchronous variants
can use a global convergence procedure which acts as a global synchronization
point. In the asynchronous model, the convergence detection is more tricky as
architectures are often very important. So, prior to deployment 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 produced
-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.
+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}
