# Tent pitching and Trefftz-DG method for the acoustic wave equation

## TL;DR

This paper introduces a space-time Trefftz discontinuous Galerkin method for efficiently solving the acoustic wave equation on tent pitched meshes, enabling local and parallel computations in heterogeneous media.

## Contribution

It develops a semi-explicit DG Trefftz method on tent pitched meshes, with implementation details and parallelization strategies for heterogeneous media.

## Key findings

- Efficient local solution of acoustic wave equation using tent pitched meshes.
- Parallel implementation in NGSolve enhances computational speed.
- Method effectively handles heterogeneous media.

## 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.