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

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 t...

Full description

Saved in:
Bibliographic Details
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
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0045-7825
DOI:10.1016/j.cma.2017.08.039