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STABLE PARAREAL IN TIME METHOD FOR FIRST AND SECOND ORDER HYPERBOLIC SYSTEM

Xiaoying Dai 1, Yvon Maday 2

(31/12/2011)

The parareal in time algorithm allows to perform parallel simulations of time dependent problems. This algorithm has been implemented on many types of time dependent problems with some success. Recent contributions have allowed to extend the domain of application of the parareal in time algorithm so as to handle long time simulations of Hamiltonian systems. This improvement has managed to avoid the fatal large lack of accuracy of the plain parareal in time algorithm consequence of the fact that the plain parareal in time algorithm does not conserve invariants. A somehow similar difficulty occurs for problems where the solution lacks regularity, either initially or in the evolution, like for the solution to hyperbolic system of conservation laws. In this paper we identify the problem of lack of stability of the parareal in time algorithm and propose a simple way to cure it. The new method is used to solve a linear wave equation and a non linear Burger's equation, the results illustrate the stability of this variant of the parareal in time algorithm.

1 :	Institute of Computational Mathematics and Scientific/Engineering Computing
	Chinese Academy of Sciences
2 :	Laboratoire Jacques-Louis Lions (LJLL)
	CNRS : UMR7598 – Université Pierre et Marie Curie [UPMC] - Paris VI

Équipe de recherche : LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

Domaine

:

Mathématiques/Analyse numérique

Mots Clés : parareal in time algorithm – parallelisation – time discretization – evolution equations – hyperbolic system – wave equation.

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Contributeur : Yvon Maday <>

Soumis le : Dimanche 1 Janvier 2012, 13:55:51

Dernière modification le : Lundi 2 Janvier 2012, 06:23:13