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Title: A space–time quasi-Trefftz DG method for the wave equation with piecewise-smooth coefficients
Trefftz methods are high-order Galerkin schemes in which all discrete functions are elementwise solution of the PDE to be approximated. They are viable only when the PDE is linear and its coefficients are piecewise-constant. We introduce a “quasi-Trefftz” discontinuous Galerkin (DG) method for the discretisation of the acoustic wave equation with piecewise-smooth material parameters: the discrete functions are elementwise approximate PDE solutions. We show that the new discretisation enjoys the same excellent approximation properties as the classical Trefftz one, and prove stability and high-order convergence of the DG scheme. We introduce polynomial basis functions for the new discrete spaces and describe a simple algorithm to compute them. The technique we propose is inspired by the generalised plane waves previously developed for time-harmonic problems with variable coefficients; it turns out that in the case of the time-domain wave equation under consideration the quasi-Trefftz approach allows for polynomial basis functions.  more » « less
Award ID(s):
2105487
PAR ID:
10443206
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Mathematics of Computation
Volume:
92
Issue:
341
ISSN:
0025-5718
Page Range / eLocation ID:
1211 to 1249
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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