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.

翻译：我们提出了一个时空Trefftz不连续的Galerkin方法,以近似音波方程式半直径地放在帐篷的阵形上。 DG Trefftz 方法使用不连续的测试和试验功能,这些功能可以解决当地波方程式的当地问题。 Tent 投球的Meshes 能够解决方程式元素问题, 从而在时间上实现本地的最佳进步。 该方法在NGSolve 中实施, 尽可能平行地解决时空元素问题。 给执行过程提供了详细信息, 包括不同媒体的传播情况 。