On wave based weak Trefftz discontinuous Galerkin approach for medium-frequency heterogeneous Helmholtz problem

• Published in: Computer methods in applied mechanics and engineering 2018-01, Vol.328, p.201-216
• Main Authors: Li, Hao, Ladevèze, Pierre, Riou, Hervé
• Format: Article
• Language: English
• Subjects: Acoustics; Engineering Sciences; Finite element analysis; Finite element method; Galerkin method; Helmholtz equations; Mathematics; Mechanical engineering; Mechanics; Trefftz method
• ISSN: 0045-7825
• DOI: 10.1016/j.cma.2017.08.039

Medium frequency heterogeneous Helmholtz problem gives rise to severe numerical challenge to Finite Element Method (FEM). An extended Variational Theory of Complex Rays (VTCR) is developed for solving this problem. Since VTCR is kind of Trefftz method, analytic solutions of governing equation need to be known a priori. But this requirement limits the application of VTCR to some specific forms of governing equations. Recently, a new computational method named weak Trefftz discontinuous Galerkin method (WTDG) is proposed to enable hybrid Finite Element method (FEM)/ Variational Theory of Complex Rays (VTCR) strategies to be developed easily in acoustics and vibrations. This hybrid method combines the advantages of FEM and VTCR to solve efficiently low frequency and medium frequency problems. This paper proposes a wave based WTDG for heterogeneous Helmholtz problem. Without knowing analytic solution of governing equation, WTDG method provides a simple and general resolution strategy for medium frequency heterogeneous Helmholtz problem.