A high-order Nystrom discretization scheme for boundary integral equations defined on rotationally symmetric surfaces

JOURNAL OF COMPUTATIONAL PHYSICS

卷:231

Article

Hao, S.¹  Martinsson, P. G.¹ 

[1] Univ Colorado, Dept Appl Math, Boulder, CO 80309 USA

关键词: Boundary integral equation;    High order discretization;    Nystrom discretization;    Body of revolution;    Scattering;    Direct solver;   

DOI  :  10.1016/j.jcp.2012.02.008

来源: Elsevier

【 摘 要 】

A scheme for rapidly and accurately computing solutions to boundary integral equations (BIEs) on rotationally symmetric surfaces in R-3 is presented. The scheme uses the Fourier transform to reduce the original BIE defined on a surface to a sequence of BIEs defined on a generating curve for the surface. It can handle loads that are not necessarily rotationally symmetric. Nystrom discretization is used to discretize the BIEs on the generating curve. The quadrature is a high-order Gaussian rule that is modified near the diagonal to retain high-order accuracy for singular kernels. The reduction in dimensionality, along with the use of high-order accurate quadratures, leads to small linear systems that can be inverted directly via, e. g., Gaussian elimination. This makes the scheme particularly fast in environments involving multiple right hand sides. It is demonstrated that for BIEs associated with the Laplace and Helmholtz equations, the kernel in the reduced equations can be evaluated very rapidly by exploiting recursion relations for Legendre functions. Numerical examples illustrate the performance of the scheme; in particular, it is demonstrated that for a BIE associated with Laplace's equation on a surface discretized using 320,800 points, the setup phase of the algorithm takes 1 min on a standard laptop, and then solves can be executed in 0.5 s. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

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