A Symmetric Trefftz-DG formulation based on a local boundary element method for the solution of the Helmholtz equation

Hélène Barucq (1) , Abderrahmane Bendali (2, 3) , M'Barek Fares (3) , Vanessa Mattesi (4, 1) , Sébastien Tordeux (1, 4)

1 Magique 3D - Advanced 3D Numerical Modeling in Geophysics
2 IMT - Institut de Mathématiques de Toulouse UMR5219
3 CERFACS - Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique
4 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

A general symmetric Trefftz Discontinuous Galerkin method is built for solving the Helmholtz equation with piecewise constant coefficients. The construction of the corresponding local solutions to the Helmholtz equation is based on a boundary element method. A series of numerical experiments displays an excellent stability of the method relatively to the penalty parameters, and more importantly its outstanding ability to reduce the instabilities known as the pollution effect in the literature on numerical simulations of long-range wave propagation.

Mots clés: integral equations; ultra-weak variational formulation; Helmholtz equation; pollution effect; dispersion; Trefftz method; Discontinuous Galerkin method; Boundary Element Method; Dirichlet-to-Neumann; pollution effect; dispersion; Trefftz method; Discontinuous Galerkin method; Boundary Element Method

Domaines: Analyse numérique [math.NA]

Hélène Barucq, Abderrahmane Bendali, M'Barek Fares, Vanessa Mattesi, Sébastien Tordeux. A Symmetric Trefftz-DG formulation based on a local boundary element method for the solution of the Helmholtz equation. Journal of Computational Physics, 2017, 330, pp.1069-1092. ⟨10.1016/j.jcp.2016.09.062⟩. ⟨hal-01395861⟩