Trefftz Discontinuous Galerkin Approximation of an Acoustic Waveguide

Abstract

SIAM Journal on Numerical Analysis, Volume 63, Issue 4, Page 1561-1585, August 2025.
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 [math] and [math]-convergence in the [math] 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).