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P Bettess

Publications and source records attributed to P Bettess.

2 recordsLinked to original sources
PubMed2004

Short-wave scattering: problems and techniques.

The paper reviews the problem of modelling short-wave scattering. Short waves are understood to be waves in which the wavelength is much smaller than any other parameters in the problem. The background to wave problems is briefly described. The major numerical methods for wave modelling, finite elements, finite differences, boundary integrals and their variants are then outlined. The recent developments in algorithms in these fields are then very briefly summarized, as an introduction to the more specialized papers to come.

Journal Article↗
PubMed2004

Plane-wave basis finite elements and boundary elements for three-dimensional wave scattering.

Classical finite-element and boundary-element formulations for the Helmholtz equation are presented, and their limitations with respect to the number of variables needed to model a wavelength are explained. A new type of approximation for the potential is described in which the usual finite-element and boundary-element shape functions are modified by the inclusion of a set of plane waves, propagating in a range of directions evenly distributed on the unit sphere. Compared with standard piecewise polynomial approximation, the plane-wave basis is shown to give considerable reduction in computational complexity. In practical terms, it is concluded that the frequency for which accurate results can be obtained, using these new techniques, can be up to 60 times higher than that of the conventional finite-element method, and 10 to 15 times higher than that of the conventional boundary-element method.

Journal Article↗