FE mode-matching schemes for the exterior Helmholtz problem and their relationship to the FE-DtN approach
FE mode-matching schemes for the exterior Helmholtz problem and their relationship to the FE-DtN approach
Finite element (FE) mode-matching procedures for the solution of Helmholtz' equation on an unbounded domain are reviewed and a symmetric general formulation is presented. This is a formal restatement of procedures applied previously to computations involving scattering of shallow water waves, acoustic transmission in non-uniform ducts and acoustic radiation from prismatic sheet metal ducts. An essential feature of the method is the use of a Galerkin procedure, rather than collocation, to match a finite computational model to a truncated modal expansion with the desired radiation characteristics. The method produces a symmetric set of linear equations which can be solved to give the unknown nodal values of the dependent variable and the modal coefficients of an outer expansion. Either of these sets of variables can be eliminated prior to solution to yield a reduced set of equations in the remaining parameters. The reduced equations obtained by eliminating the modal coefficients are shown to be identical to those obtained by applying a truncated Dirichlet-to-Neumann (DtN) boundary condition. If applied in this form, mode-matching can therefore be regarded as an alternative to the DtN method for generating this common set of discrete equations while permitting simultaneous solution for the modal coefficients in the outer region.
mode-matching, helmholtz, equation, dtn, finite element
257-267
Astley, R.J.
cb7fed9f-a96a-4b58-8939-6db1010f9893
April 1996
Astley, R.J.
cb7fed9f-a96a-4b58-8939-6db1010f9893
Astley, R.J.
(1996)
FE mode-matching schemes for the exterior Helmholtz problem and their relationship to the FE-DtN approach.
[in special issue: Communications in Numerical Methods in Engineering]
International Journal for Numerical Methods in Biomedical Engineering, 12 (4), .
(doi:10.1002/(SICI)1099-0887(199604)).
Abstract
Finite element (FE) mode-matching procedures for the solution of Helmholtz' equation on an unbounded domain are reviewed and a symmetric general formulation is presented. This is a formal restatement of procedures applied previously to computations involving scattering of shallow water waves, acoustic transmission in non-uniform ducts and acoustic radiation from prismatic sheet metal ducts. An essential feature of the method is the use of a Galerkin procedure, rather than collocation, to match a finite computational model to a truncated modal expansion with the desired radiation characteristics. The method produces a symmetric set of linear equations which can be solved to give the unknown nodal values of the dependent variable and the modal coefficients of an outer expansion. Either of these sets of variables can be eliminated prior to solution to yield a reduced set of equations in the remaining parameters. The reduced equations obtained by eliminating the modal coefficients are shown to be identical to those obtained by applying a truncated Dirichlet-to-Neumann (DtN) boundary condition. If applied in this form, mode-matching can therefore be regarded as an alternative to the DtN method for generating this common set of discrete equations while permitting simultaneous solution for the modal coefficients in the outer region.
This record has no associated files available for download.
More information
Published date: April 1996
Keywords:
mode-matching, helmholtz, equation, dtn, finite element
Identifiers
Local EPrints ID: 166673
URI: http://eprints.soton.ac.uk/id/eprint/166673
ISSN: 2040-7947
PURE UUID: c6ce9d53-314d-4a1a-a7a9-1e7ca78d7f01
Catalogue record
Date deposited: 01 Nov 2010 13:40
Last modified: 14 Mar 2024 02:14
Export record
Altmetrics
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics