The University of Southampton
University of Southampton Institutional Repository

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
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
2040-7947
257-267
Astley, R.J.
cb7fed9f-a96a-4b58-8939-6db1010f9893
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), 257-267. (doi:10.1002/(SICI)1099-0887(199604)).

Record type: Article

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

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×