Tent pitching and Trefftz-DG method for the acoustic wave equation
arXiv:1907.02367 · doi:10.1016/j.camwa.2020.01.006
Abstract
We present a space-time Trefftz discontinuous Galerkin method for approximating the acoustic wave equation semi-explicitly on tent pitched meshes. DG Trefftz methods use discontinuous test and trial functions, which solve the wave equation locally. Tent pitched meshes allow to solve the equation elementwise, allowing locally optimal advances in time. The method is implemented in NGSolve, solving the space-time elements in parallel, whenever possible. Insights into the implementational details are given, including the case of propagation in heterogeneous media.
arXiv comment18 pages, 11 figures
References in corpus (4)
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Cited by in corpus (5)
- A space-time quasi-Trefftz DG method for the wave equation with piecewise-smooth coefficients
- On the space-time discretization of variational retarded potential boundary integral equations
- Discrete conservation laws for finite element discretisations of multisymplectic PDEs
- Space-time discontinuous Galerkin approximation of acoustic waves with point singularities
- A space-time Trefftz discontinuous Galerkin method for the linear Schrödinger equation