期刊
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
卷 204, 期 2, 页码 363-374出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cam.2006.03.029
关键词
high frequency scattering; acoustics; oscillatory integrals; method of stationary phase
We consider the approximation of some highly oscillatory weakly singular surface integrals, arising from boundary integral methods with smooth global basis functions for solving problems of high frequency acoustic scattering by three-dimensional convex obstacles, described globally in spherical coordinates. As the frequency of the incident wave increases, the performance of standard quadrature schemes deteriorates. Naive application of asymptotic schemes also fails due to the weak singularity. We propose here a new scheme based on a combination of an asymptotic approach and exact treatment of singularities in an appropriate coordinate system. For the case of a spherical scatterer we demonstrate via error analysis and numerical results that, provided the observation point is sufficiently far from the shadow boundary, a high level of accuracy can be achieved with a minimal computational cost. (c) 2006 Elsevier B.V. All rights reserved.
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