Work

Trefftz Discontinuous Galerkin Approximation of an Acoustic Waveguide

Year: 2025

Type: article

Abstract: . We propose a modified Trefftz discontinuous Galerkin (TDG) method for approximating a time-harmonic acoustic scattering problem in an infinitely elongated waveguide. In the waveguide we suppose that there is a bounded, penetrable, and possibly absorbing scatterer. The classical TDG is not applicable when the scatterer is absorbing. Novel features of our modified TDG method are that it is applicable in this case, and it uses a stable treatment of the outgoing radiation condition for the scattered field. For the modified TDG, we prove [Formula: see text] and [Formula: see text]-convergence in the [Formula: see text] norm for nonabsorbing scatterers. The theoretical results are verified numerically for a discretization based on plane waves, and also investigated numerically for absorbing scatterers (in which case the plane waves are evanescent in the scatterer).

Source: SIAM Journal on Numerical Analysis

DOI: 10.1137/24m1686905

Authors: Peter Monk, Manuel Pena, Virginia Selgas

Institutions: University of Delaware, Universidade de Vigo, Universidad de Oviedo

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green