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A numerical integration scheme for special finite elements for the Helmholtz equation

A numerical integration scheme for special finite elements for the Helmholtz equation
A numerical integration scheme for special finite elements for the Helmholtz equation
The theory for integrating the element matrices for rectangular, triangular and quadrilateral finite elements for the solution of the Helmholtz equation for very short waves is presented. A numerical integration scheme is developed. Samples of Maple and Fortran code for the evaluation of integration abscissæ and weights are made available. The results are compared with those obtained using large numbers of Gauss-Legendre integration points for a range of testing wave problems. The results demonstrate that the method gives correct results, which gives confidence in the procedures, and show that large savings in computation time can be achieved.
short waves, finite elements, special finite elements, semi-analytical integration, numerical integration, partition of unity method (pum)
0029-5981
531-552
Bettess, P.
97ac23e0-6e16-408a-91c8-fcba3b35a829
Shirron, J.
4c39715a-f341-4e51-9584-35bf0b1d590d
Laghrouche, O.
6876d805-adbb-43ca-aa04-05692aa8384b
Peseux, B.
aa23facd-7afe-4264-b9e2-a07b6aad4635
Sugimoto, R.
cb8c880d-0be0-4efe-9990-c79faa8804f0
Trevelyan, J.
95ad8711-55ca-409d-bbed-055788116df7
Bettess, P.
97ac23e0-6e16-408a-91c8-fcba3b35a829
Shirron, J.
4c39715a-f341-4e51-9584-35bf0b1d590d
Laghrouche, O.
6876d805-adbb-43ca-aa04-05692aa8384b
Peseux, B.
aa23facd-7afe-4264-b9e2-a07b6aad4635
Sugimoto, R.
cb8c880d-0be0-4efe-9990-c79faa8804f0
Trevelyan, J.
95ad8711-55ca-409d-bbed-055788116df7

Bettess, P., Shirron, J., Laghrouche, O., Peseux, B., Sugimoto, R. and Trevelyan, J. (2003) A numerical integration scheme for special finite elements for the Helmholtz equation. International Journal for Numerical Methods in Engineering, 56 (4), 531-552. (doi:10.1002/nme.575).

Record type: Article

Abstract

The theory for integrating the element matrices for rectangular, triangular and quadrilateral finite elements for the solution of the Helmholtz equation for very short waves is presented. A numerical integration scheme is developed. Samples of Maple and Fortran code for the evaluation of integration abscissæ and weights are made available. The results are compared with those obtained using large numbers of Gauss-Legendre integration points for a range of testing wave problems. The results demonstrate that the method gives correct results, which gives confidence in the procedures, and show that large savings in computation time can be achieved.

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More information

Published date: 2003
Keywords: short waves, finite elements, special finite elements, semi-analytical integration, numerical integration, partition of unity method (pum)

Identifiers

Local EPrints ID: 10386
URI: https://eprints.soton.ac.uk/id/eprint/10386
ISSN: 0029-5981
PURE UUID: 4bcd03e5-1547-4e16-a58c-6173d65febcb

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Date deposited: 25 Jul 2005
Last modified: 17 Jul 2017 17:07

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