Tent pitching and Trefftz-DG method for the acoustic wave equation. (15th May 2020)

• Record Type: Journal Article
• Authors: Perugia, Ilaria; Schöberl, Joachim; Stocker, Paul; Wintersteiger, Christoph
• Is Part Of: Computers & mathematics with applications. Volume 79:issue 10(2020)
• Page Start: 2987
• Page End: 3000
• Publication Date: 2020-05-15
• Subjects: Wave equation -- Discontinuous Galerkin method -- Trefftz method -- Tent pitched mesh; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2020.01.006
• Languages: English
• ISSNs: 0898-1221

Abstract

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 us 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.