Open Access

ARTICLE

A Spectral Boundary Element Method for Scattering Problems

J. Tausch¹, J. Xiao²

1 Southern Methodist University, Department of Mathematics, Dallas, TX, USA
2 College of Astronautics, Northwestern Polytechnical University, Xi’an 710072, China

Computer Modeling in Engineering & Sciences 2010, 58(3), 221-246. https://doi.org/10.3970/cmes.2010.058.221

Abstract

A fast method for the computation of layer potentials that arise in acoustic scattering is introduced. The principal idea is to split the singular kernel into a smooth and a local part. The potential due to the smooth part is discretized by a Nyström method and is evaluated efficiently using a sequence of FFTs. The potential due to the local part is approximated by a truncated series in the mollification parameter. The smooth approximation of the kernel is obtained by multiplication of its Fourier transform with a filter. We will show that for a rational filter the smooth part and the expansion coefficients of the local part can be found in closed form. The accuracy of the method is determined by the number of Fourier modes, the mollification parameter and the mesh width of discretization. We will investigate how to choose the parameters as a function of the wave number. The effectiveness of the method is illustrated for medium-sized scatterers (50-100 wavelengths) that may have complicated geometry.

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