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A comparison of two wave element methods for the Helmholtz problem

A comparison of two wave element methods for the Helmholtz problem
A comparison of two wave element methods for the Helmholtz problem
In comparison with low-order finite element methods (FEMs), the use of oscillatory basis functions has been shown to reduce the computational complexity associated with the numerical approximation of Helmholtz problems at high wave numbers. We compare two different wave element methods for the 2D Helmholtz problems. The methods chosen for this study are the partition of unity FEM (PUFEM) and the ultra-weak variational formulation (UWVF). In both methods, the local approximation of wave field is computed using a set of plane waves for constructing the basis functions. However, the methods are based on different variational formulations; the PUFEM basis also includes a polynomial component, whereas the UWVF basis consists purely of plane waves. As model problems we investigate propagating and evanescent wave modes in a duct with rigid walls and singular eigenmodes in an L-shaped domain. Results show a good performance of both methods for the modes in the duct, but only a satisfactory accuracy was obtained in the case of the singular field. On the other hand, both the methods can suffer from the ill-conditioning of the resulting matrix system.
Helmholtz problem, partition of unity, ultra-weak variational formulation
1069-8299
35-52
Huttunen, T.
014b99e4-1caa-47d9-a283-705c60cf4c12
Gamallo, P.
4a10847b-5368-4f60-aab6-19a80b8556c9
Astley, R.J.
cb7fed9f-a96a-4b58-8939-6db1010f9893
Huttunen, T.
014b99e4-1caa-47d9-a283-705c60cf4c12
Gamallo, P.
4a10847b-5368-4f60-aab6-19a80b8556c9
Astley, R.J.
cb7fed9f-a96a-4b58-8939-6db1010f9893

Huttunen, T., Gamallo, P. and Astley, R.J. (2009) A comparison of two wave element methods for the Helmholtz problem. Communications in Numerical Methods in Engineering, 25 (1), 35-52. (doi:10.1002/cnm.1102).

Record type: Article

Abstract

In comparison with low-order finite element methods (FEMs), the use of oscillatory basis functions has been shown to reduce the computational complexity associated with the numerical approximation of Helmholtz problems at high wave numbers. We compare two different wave element methods for the 2D Helmholtz problems. The methods chosen for this study are the partition of unity FEM (PUFEM) and the ultra-weak variational formulation (UWVF). In both methods, the local approximation of wave field is computed using a set of plane waves for constructing the basis functions. However, the methods are based on different variational formulations; the PUFEM basis also includes a polynomial component, whereas the UWVF basis consists purely of plane waves. As model problems we investigate propagating and evanescent wave modes in a duct with rigid walls and singular eigenmodes in an L-shaped domain. Results show a good performance of both methods for the modes in the duct, but only a satisfactory accuracy was obtained in the case of the singular field. On the other hand, both the methods can suffer from the ill-conditioning of the resulting matrix system.

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Published date: 2009
Keywords: Helmholtz problem, partition of unity, ultra-weak variational formulation
Organisations: Civil Engineering & the Environment, Fluid Dynamics & Acoustics Group

Identifiers

Local EPrints ID: 79178
URI: http://eprints.soton.ac.uk/id/eprint/79178
ISSN: 1069-8299
PURE UUID: a08a2c90-ec60-4216-a000-c75d2e724b33

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Date deposited: 12 Mar 2010
Last modified: 14 Mar 2024 00:28

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Contributors

Author: T. Huttunen
Author: P. Gamallo
Author: R.J. Astley

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