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Behavior of parallel two-stage method for the simulation of steel solidification in continuous casting

ADVANCES IN ENGINEERING SOFTWARE 2019年 131卷 116-142页

作者： Garcia, T. Spiteri, P. Khenniche, G. Univ Toulouse IRIT INPT 2 Rue Charles CamichelBP 7122 F-31071 Toulouse 7 France Univ Toulouse IRIT INPT ENSEEIHT 2 Rue Charles CamichelBP 7122 F-31071 Toulouse 7 France Skikda Univ Lab LAMAHIS Dept Math Fac Sci Skikda Algeria

This paper presents the behavior of general parallel synchronous and asynchronous multisplitting and two-stage methods for the numerical simulation of steel solidification in continuous casting. Thanks to the mathematical analysis and the implementation of these methods one can show the results of parallel experiments for the target application. The mathematical model is constituted by coupled nonlinear boundary value problems, namely the heat equation taking into account, on part of the boundary, a radiation phenomenon described by the Stefan law. For the numerical solution of such partial differential equations we consider, depending on whether the coefficient of thermal conductivity is constant or temperature-dependent, both an implicit or a semi-implicit discretization with respect to the time of the studied evolution problem, while the spatial discretization is carried out by adapted finite difference schemes. Then large scale discretized algebraic systems are solved by sequential and synchronous or asynchronous iterative algorithms;comparison of these various previous methods implemented on clusters and grid are achieved in both cases when the thermal conductivity is constant and more generally dependent of the temperature.

关键词： Continuous casting Sparse non-linear systems synchronous parallel algorithms Asynchronous parallel algorithms Multisplitting methods Two-stage methods

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Coupling parallel asynchronous multisplitting methods with Krylov methods to solve pseudo-linear evolution 3D problems

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JOURNAL OF COMPUTATIONAL SCIENCE 2021年 51卷 101303-101303页

作者： Garcia, T. Spiteri, P. Ziane-Khodja, L. Couturier, R. Univ Toulouse IRIT INPT 2 Rue Charles CamichelBP 122 F-31071 Toulouse 7 France Univ Toulouse IRIT INPT ENSEEIHT 2 Rue Charles CamichelBP 7122 F-31071 Toulouse 7 France ANEO 122 Ave Gen Leclerc F-92100 Boulogne France Univ Bourgogne Franche Comte CNRS FEMTO ST Inst 19 Av Marechal JuinBP 527 F-90016 Belfort France

The present study deals with pseudo-linear problems solving using parallel asynchronous multisplitting methods combined with Krylov methods. With appropriate and realistic assumptions, the behavior of such parallel iterative algorithms will be analyzed by partial ordering techniques in relation with the discrete maximum principle. Applications to discretized boundary value problems are presented, the implementation of the algorithms is described and parallel experiments are analyzed.

关键词： Multisplitting methods synchronous parallel algorithms Asynchronous parallel algorithms Sparse non-linear systems Krylov methods Pseudo-linear problem Principle of discrete maximum Boundary value problem

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Solution of univalued and multivalued pseudo-linear problems using parallel asynchronous multisplitting methods combined with Krylov methods

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ADVANCES IN ENGINEERING SOFTWARE 2021年 153卷 102929-102929页

作者： Garcia, T. Spiteri, P. Ziane-Khodja, L. Couturier, R. Univ Toulouse IRIT INPT 2 Rue Charles CamichelBP 7122 F-31071 Toulouse 7 France Univ Toulouse IRIT INPT ENSEEIHT 2 Rue Charles CamichelBP 7122 F-31071 Toulouse 7 France ANEO 122 Ave Gen Leclerc F-92100 Boulogne France Univ Bourgogne Franche Comte CNRS FEMTO ST Inst 19 Ave Marchal JuinBP 527 F-90016 Belfort France

The paper improves a preliminary experimental study on a cluster by adding both theoretical results and experimental tests on a grid platform. These algorithms solve univalued and multivalued pseudo-linear problems using parallel asynchronous multisplitting methods combined with Krylov's methods. This paper also analyses these algorithms using contraction techniques. Two distinct applications, with discretized boundary value problems, are analyzed and simulated. First, a univalued convection-diffusion problem perturbed by an increasing diagonal operator is presented. Then, follows the description of a diffusion problem whose solution is constrained. This situation classically leads to the solution of a multivalued pseudo-linear problem in which the linear part is perturbed by an increasing diagonal multivalued operator. parallel asynchronous and synchronous algorithms were implemented and tested on a grid platform composed of physically adjacent or geographically distant machines. In addition, the simulation results are detailed and show that the elapsed times obtained for the asynchronous algorithms are significantly less than those obtained for the synchronous algorithms.

关键词： multisplitting methods synchronous parallel algorithms asynchronous parallel algorithms sparse non-linear systems Krylov methods pseudo - liner problem boundary value problem

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