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Three‐dimensional discontinuous Galerkin elements with plane waves and Lagrange multipliers for the solution of mid‐frequency Helmholtz problems
Author(s) -
Tezaur Radek,
Farhat Charbel
Publication year - 2006
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1575
Subject(s) - lagrange multiplier , discontinuous galerkin method , helmholtz equation , galerkin method , helmholtz free energy , mathematics , mathematical analysis , finite element method , plane wave , basis function , plane (geometry) , degrees of freedom (physics and chemistry) , geometry , mathematical optimization , boundary value problem , physics , quantum mechanics , optics , thermodynamics
Recently, a discontinuous Galerkin finite element method with plane wave basis functions and Lagrange multiplier degrees of freedom was proposed for the efficient solution in two dimensions of Helmholtz problems in the mid‐frequency regime. In this paper, this method is extended to three dimensions and several new elements are proposed. Computational results obtained for several wave guide and acoustic scattering model problems demonstrate one to two orders of magnitude solution time improvement over the higher‐order Galerkin method. Copyright © 2005 John Wiley & Sons, Ltd.