of asynchronous iterative algorithms. For that, we compare the behaviour of a
synchronous GMRES algorithm with an asynchronous multisplitting one with
simulations which let us easily choose some parameters. Both codes are real MPI
of asynchronous iterative algorithms. For that, we compare the behaviour of a
synchronous GMRES algorithm with an asynchronous multisplitting one with
simulations which let us easily choose some parameters. Both codes are real MPI
$X_{0}$ to find an approximate value $X^*$ of the solution with a very low residual error. Several well-known methods
demonstrate the convergence of these algorithms~\cite{BT89,Bahi07}.
$X_{0}$ to find an approximate value $X^*$ of the solution with a very low residual error. Several well-known methods
demonstrate the convergence of these algorithms~\cite{BT89,Bahi07}.
into several \emph{blocks} that will be solved in parallel on multiple
processing units. The latter will communicate each intermediate results before a
new iteration starts and until the approximate solution is reached. These
into several \emph{blocks} that will be solved in parallel on multiple
processing units. The latter will communicate each intermediate results before a
new iteration starts and until the approximate solution is reached. These
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
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
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
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,
+nodes, inter and intra clusrters bandwith and latency, etc.) and of the
+algorithm (number of splittings with the multisplitting algorithm), the
+multisplitting code will obtain the solution more or less quickly. Of 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
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
framework to study the behavior of large-scale distributed systems. As its name
says, it emanates from the grid computing community, but is nowadays used to
study grids, clouds, HPC or peer-to-peer systems. The early versions of SimGrid
framework to study the behavior of large-scale distributed systems. As its name
says, it emanates from the grid computing community, but is nowadays used to
study grids, clouds, HPC or peer-to-peer systems. The early versions of SimGrid
-date from 1999, but it's still actively developed and distributed as an open
-source software. Today, it's one of the major generic tools in the field of
+date from 1999, but it is still actively developed and distributed as an open
+source software. Today, it is one of the major generic tools in the field of
simulation for large-scale distributed systems.
SimGrid provides several programming interfaces: MSG to simulate Concurrent
simulation for large-scale distributed systems.
SimGrid provides several programming interfaces: MSG to simulate Concurrent
- \includegraphics[width=60mm,keepaspectratio]{clustering}
-\caption{Example of three clusters of processors interconnected by a virtual unidirectional ring network.}
+ \includegraphics[width=60mm,keepaspectratio]{clustering2}
+\caption{Example of two distant clusters of processors.}
%Then we have changed the network configuration using three clusters containing
%respectively 33, 33 and 34 hosts, or again by on hundred hosts for all the
%clusters. In the same way as above, a judicious choice of key parameters has
%permitted to get the results in Table~\ref{tab.cluster.3x33} which shows the
%relative gains greater than 1 with a matrix size from 62 to 100 elements.
%Then we have changed the network configuration using three clusters containing
%respectively 33, 33 and 34 hosts, or again by on hundred hosts for all the
%clusters. In the same way as above, a judicious choice of key parameters has
%permitted to get the results in Table~\ref{tab.cluster.3x33} which shows the
%relative gains greater than 1 with a matrix size from 62 to 100 elements.
-\CER{En accord avec RC, on a pour le moment enlevé les tableaux 2 et 3 sachant que les résultats obtenus sont limites. De même, on a enlevé aussi les deux dernières colonnes du tableau I en attendant une meilleure performance et une meilleure precision}
+%\CER{En accord avec RC, on a pour le moment enlevé les tableaux 2 et 3 sachant que les résultats obtenus sont limites. De même, on a enlevé aussi les deux dernières colonnes du tableau I en attendant une meilleure performance et une meilleure precision}
- \item Intra-cluster network bandwidth: \np[Gbit/s]{1.25} and latency: \np[$\mu$s]{0.05};
- \item Inter-cluster network bandwidth: \np[Mbit/s]{5} or \np[Mbit/s]{50} and latency: \np[$\mu$s]{20};
+ \item Intra-cluster network bandwidth: \np[Gbit/s]{1.25} and latency: \np[$\mu$s]{50};
+ \item Inter-cluster network bandwidth: \np[Mbit/s]{5} or \np[Mbit/s]{50} and latency: \np[ms]{20};
