On Adaptive Definition of the Plane Wave Basis for Wave Boundary Elements in Acoustic Scattering: the 2D Case
J. Trevelyan; and G. Coates

doi:10.3970/cmes.2010.055.147
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 55, No. 2, pp. 147-170, 2010
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Keywords wave scattering, plane wave basis, boundary integral equation, boundary elements, adaptivity.
Abstract The terminology "wave boundary elements" relates to boundary elements enriched in the Partition of Unity sense by a multiple plane wave basis for the analysis of the propagation of short wavelength waves. This paper presents a variant of this approach in which the plane wave basis is selected adaptively according to an error indicator. The error indicator is residual based, and exhibits useful local and global properties. Model improvement in each adaptive iteration is carried out by the addition of new plane waves with no h-refinement. The convergence properties of the scheme are demonstrated.
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