Study of Physics-Based preconditioning with High-order Galerkin discretization for hyperbolic wave problems

Clémentine Courtès (1) , Emmanuel Franck (2) , Philippe Helluy (2, 3) , Herbert Oberlin (4)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 TONUS - TOkamaks and NUmerical Simulations
3 IRMA - Institut de Recherche Mathématique Avancée
4 IPP - Max-Planck-Institut für Plasmaphysik [Garching]

In this article, we detail the construction of a physics-based preconditioner. The Schur decomposition is the key point of the method which is tested on two hyperbolic systems : acoustic wave equations and shallow water equations without source term. Some conserved properties between preconditioner and initial operator are discussed, especially the propagation speeds of a plane wave.

Mots clés: implicit; hyperbolic system; galerkin; preconditioning

Domaines: Analyse numérique [math.NA]

Clémentine Courtès, Emmanuel Franck, Philippe Helluy, Herbert Oberlin. Study of Physics-Based preconditioning with High-order Galerkin discretization for hyperbolic wave problems. ESAIM: Proceedings and Surveys, 2017, ⟨10.1051/proc/201655061⟩. ⟨hal-01401547⟩