Reducing spurious dispersion, anisotropy and reflection in finite element analysis of time-harmonic acoustics

Isaac Harari*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

53 Scopus citations

Abstract

Galerkin and stabilized (Galerkin/least-squares and Galerkin/gradient least-squares) finite element methods for solving problems of time-harmonic acoustics are presented and analyzed. The error of discretization is related to spurious representation of physical phenomena, namely dispersion, anisotropy and reflection, all of which decrease with mesh refinement. The performance of the stabilized methods in terms of dispersion and anisotropy is identical, both are superior to the Galerkin method, relaxing wave resolution requirements. Further insight into the design of these methods is provided by the analyses. The stabilized methods differ in the degree of spurious reflection that is engendered by transitions in mesh size. The performance of Galerkin/gradient least-squares deteriorates on non-uniform meshes. However, Galerkin/least-squares maintains its enhanced performance, exhibiting low sensitivity to transitions in mesh size, thereby reducing spurious dispersion, anisotropy and reflection in finite element analysis of time-harmonic acoustics. Guidelines for discretization pertaining to mesh orientation and wave resolution are presented.

Original languageEnglish
Pages (from-to)39-58
Number of pages20
JournalComputer Methods in Applied Mechanics and Engineering
Volume140
Issue number1-2
DOIs
StatePublished - 15 Jan 1997

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