PML applied to spacetime Trefftz-DG numerical formulation for the acoustic wave equation

Vinduja Vasanthan

In the first part of our work, we have developed a Trefftz-DG framework for solving acoustic equations using Tent Pitcher algorithms. A Trefftz-DG variational formulation applied to wave problems is a Trefftz variational formulation applied on each cell of a mesh of the domain of interest with appropriate transmission conditions between the cells. The basis functions are exact (or approximations of the) solutions, which reduces the numerical dispersion. The Tent-Pitching algorithm consists in building a space-time mesh composed of cells satisfying a causality constraint. The next part of our work consists in addressing the natural question of truncating the computational domain. For that purpose, we have constructed Perfectly Matched Layer (PML). We thus introduce a new Trefftz-DG method for the acoustic wave equation based on the use of Green’s functions as basis functions, which involves a Trefftz-DG variational formulation inside the PML in a Tent-Pitcher framework.