Titre :

A hybridizable discontinuous Galerkin method with transmission variables for time-harmonic wave problems in heterogeneous media

Auteur(s) :

Pescuma, Simone [Auteur]
Propagation des Ondes : Étude Mathématique et Simulation [POEMS]
Gabard, Gwenael [Auteur]
Laboratoire d'Acoustique de l'Université du Mans [LAUM]
Chaumont-Frelet, Théophile [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Reliable numerical approximations of dissipative systems [RAPSODI]
Modave, Axel [Auteur]
Propagation des Ondes : Étude Mathématique et Simulation [POEMS]

Discipline(s) HAL :

Mathématiques [math]/Analyse numérique [math.NA]
Informatique [cs]/Modélisation et simulation
Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Sciences de l'ingénieur [physics]/Acoustique [physics.class-ph]

Résumé en anglais : [en]

We consider the finite element solution of time-harmonic wave propagation problems in heterogeneous media with hybridizable discontinuous Galerkin (HDG) methods. In the case of homogeneous media, it has been observed that ...
Lire la suite >We consider the finite element solution of time-harmonic wave propagation problems in heterogeneous media with hybridizable discontinuous Galerkin (HDG) methods. In the case of homogeneous media, it has been observed that the iterative solution of the linear system can be accelerated by hybridizing with transmission variables instead of numerical traces, as performed in standard approaches. In this work, we extend the HDG method with transmission variables, which is called the CHDG method, to the heterogeneous case with piecewise constant physical coefficients. In particular, we consider formulations with standard upwind and general symmetric fluxes. The CHDG hybridized system can be written as a fixed-point problem, which can be solved with stationary iterative schemes for a class of symmetric fluxes. The standard HDG and CHDG methods are systematically studied with the different numerical fluxes by considering a series of 2D numerical benchmarks. The convergence of standard iterative schemes is always faster with the extended CHDG method than with the standard HDG methods, with upwind and scalar symmetric fluxes.Lire moins >

Langue :

Anglais

Projet ANR :

Méthodes d'éléments finis discontinus de type Galerkin spécifiques pour la propagation des ondes en régime harmonique

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL