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Chau M.,Advanced Solutions Accelerator | Garcia T.,National Polytechnic Institute of Toulouse | Spiteri P.,National Polytechnic Institute of Toulouse
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2011

In the present study we consider the parallel simulation on a peer-topeer demonstrator for the computation of a 3D differential equations, which model the behavior of the continuous-flow electrophoresis problem. The physical model considered is constituted by the Navier-Stokes equation coupled with a convection-diffusion equation and a Laplacian equation. By using appropriate discretization of the coupled boundary value problems, we can prove the convergence of synchronous and more generally asynchronous relaxation methods. Finally parallel experiments on the peer-to-peer demonstrator are presented and analyzed. © 2011 Springer-Verlag. Source


Khochemane H.E.,Annaba University | Boutabia H.,Annaba University | Chau M.,Advanced Solutions Accelerator | Spiteri P.,IRIT ENSEEIHT IRIT
Computers and Mathematics with Applications | Year: 2016

The present study deals with the numerical solution of the modified porous medium equation when the solution is subject to some constraints. First of all, we use a change of variables, which leads to an evolutive problem where the nonlinear part is constituted by the derivative with respect to the time, of a diagonal increasing operator. Then, for the numerical solution we consider an implicit time marching scheme, which leads to the solution of a sequence of stationary problems. In fact each stationary problem is equivalent to a constrained minimization problem, and for Dirichlet and Dirichlet-Neumann boundary conditions, we show the existence and the uniqueness of the solution of our stationary constrained minimization problem. Moreover, classically, the solution of each stationary constrained problem can be characterized by the solution of a multivalued one. The spatial discretization of the previous problem leads to the solution of large scale algebraic multivalued systems. Then we analyze in a unified approach the convergence of the sequential and parallel relaxation projected methods. Finally we present the results of numerical experiments. © 2016 Elsevier Ltd. All rights reserved. Source


Garcia T.,National Polytechnic Institute of Toulouse | Chau M.,Advanced Solutions Accelerator | Spiteri P.,National Polytechnic Institute of Toulouse
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2011

This paper deals with the numerical solution of financial applications, more specifically the computation of American and European options derivatives modeled by boundary value problems. In such applications we have to solve large-scale algebraic linear systems. We concentrate on synchronous and asynchronous parallel iterative algorithms carried out on Grid'5000, by using an experimental peer-to-peer platform. The properties of the operators arising in the discretized problem ensure the convergence of the parallel iterative synchronous and asynchronous algorithms. Different detection convergence algorithms are tested for asynchronous iterations. Computational experiments performed on distributed architectures are presented and analyzed. © 2011 Springer-Verlag. Source


Chau M.,Advanced Solutions Accelerator | Couturier R.,University of Technology of Belfort - Montbeliard | Bahi J.,University of Technology of Belfort - Montbeliard | Spiteri P.,ENSEEIHT IRIT
International Journal of High Performance Computing Applications | Year: 2011

The present study deals with the solution of the obstacle problem defined in a three-dimensional domain. In order to solve a large-scale obstacle problem, the use of parallelism is necessary. In this work we present a parallel synchronous iterative algorithm to solve this problem and its asynchronous version. For the considered problem, the convergence of parallel synchronous and asynchronous algorithms is analysed in a general framework. Finally, computational experiments on GRID'5000, the French national grid, are presented and analysed. They allow us to compare both synchronous and asynchronous versions with local and distributed clusters. © 2011 SAGE Publications. Source


Chau M.,Advanced Solutions Accelerator | Garcia T.,ENSEEIHT IRIT | Spiteri P.,ENSEEIHT IRIT
Advances in Engineering Software | Year: 2013

This paper deals with the implementation on the Grid'5000 network, the French grid platform, of parallel simulations for the solution of a 3D coupled boundary value problem. This problem models continuous flow electrophoresis which is governed by Navier Stokes equations coupled with convection-diffusion and potential equations. The coupled boundary value problems are discretised by appropriate schemes involving the convergence of the parallel synchronous and asynchronous Schwarz alternating algorithms. Finally, parallel experiments on grid computing are presented and analyzed. © 2012 Civil-Comp Ltd and Elsevier Ltd. All rights reserved. Source

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