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Use of Wave Boundary Elements for Acoustic Computations

Emmanuel Perrey-Debain

School of Engineering, University of Durham, Durham DH1 3LE, UK

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Jon Trevelyan

School of Engineering, University of Durham, Durham DH1 3LE, UK

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, and

Peter Bettess

School of Engineering, University of Durham, Durham DH1 3LE, UK

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https://doi.org/10.1142/S0218396X03001924Cited by:17 (Source: Crossref)

Abstract

Discrete methods of numerical analysis have been used successfully for decades for the solution of problems involving wave diffraction, etc. However, these methods, including the finite element and boundary element methods, can require a prohibitively large number of elements as the wavelength becomes progressively shorter. In this work, a new type of interpolation for the acoustic field is described in which the usual conventional shape functions are modified by the inclusion of a set of plane waves propagating in multiple directions. Including such a plane wave basis in a boundary element formulation has been found in the current work to be highly successful. Results are shown for a variety of classical scattering problems, and also for scattering from nonconvex obstacles. Notable results include a conclusion that, using this new formulation, only approximately 2.5 degrees of freedom per wavelength are required. Compared with the 8 to 10 degrees of freedom normally required for conventional boundary (and finite) elements, this shows the marked improvement in storage requirement. Moreover, the new formulation is shown to be extremely accurate. It is estimated that for 2D Helmholtz problems, and for a given computational resource, the frequency range allowed by this method is extended by a factor of three over conventional direct collocation Boundary Element Method. Recent successful developments of the current method for plane elastodynamics problems are also briefly outlined.

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