X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/rce2015.git/blobdiff_plain/1d3b67d64fd41314640caf3d2ff71f52d7b71181..cab574aad44572e4c4c295cd5b3d86488c332ca4:/paper.tex diff --git a/paper.tex b/paper.tex index 49480a8..4d7c9b8 100644 --- a/paper.tex +++ b/paper.tex @@ -154,7 +154,7 @@ iteration without having to wait for the data dependencies coming from its 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 @@ -181,7 +181,7 @@ multisplitting algorithm with the GMRES (Generalized Minimal RESidual) 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 @@ -209,7 +209,7 @@ concluding remarks and perspectives. 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}. @@ -219,8 +219,8 @@ studied. Otherwise, the application is not ensure to reach the convergence. An 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 @@ -239,12 +239,12 @@ optimize since the financial and deployment costs on large scale multi-core 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} -In the scope of this paper, we have chosen the SimGrid toolkit~\cite{SimGrid,casanova+giersch+legrand+al.2014.versatile} to simulate the behavior of parallel iterative linear solvers on different computational grid configurations. In opposite to the most simulators which are stayed very oriented-application, SimGrid framework is designed to study the behavior of many large-scale distributed computing platforms as Grids, Peer-to-Peer systems, Clouds or High Performance Computation systems. It is still actively developed by the scientific community and distributed as an open source software. +In the scope of this paper, we have chosen the SimGrid toolkit~\cite{SimGrid,casanova+giersch+legrand+al.2014.versatile} to simulate the behavior of parallel iterative linear solvers on different computational grid configurations. In opposite to most of the simulators which are stayed very oriented-application, the SimGrid framework is designed to study the behavior of many large-scale distributed computing platforms as Grids, Peer-to-Peer systems, Clouds or High Performance Computation systems. It is still actively developed by the scientific community and distributed as an open source software. SimGrid provides four user interfaces which can be convenient for different distributed applications~\cite{casanova+legrand+quinson.2008.simgrid}. In this paper we are interested on the SMPI user interface (Simulator MPI) which implements about \np[\%]{80} of the MPI 2.0 standard and allows minor modifications of the initial code~\cite{bedaride+degomme+genaud+al.2013.toward} (see Section~\ref{sec:04.02}). SMPI enables the direct simulation of the execution, as in the real life, of an unmodified MPI distributed application, and gets accurate results with the detailed resources consumption.