A fast numerical method for a natural boundary integral equation for the Helmholtz equation
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摘要
A Neumann boundary value problem of the Helmholtz equation in the exterior circular domain is reduced into an equivalent natural boundary integral equation. Using our trigonometric wavelets and the Galerkin method, the obtained stiffness matrix is symmetrical and circulant, which lead us to a fast numerical method based on fast Fourier transform. Furthermore, we do not need to compute the entries of the stiffness matrix. Especially, our method is also efficient when the wave number k in the Helmholtz equation is very large.
论文关键词:65N38,65F30,42C40,65T50,Natural boundary integral method,Trigonometric wavelets,Matrix decomposition,FFT,Helmholtz equation
论文评审过程:Received 19 March 2008, Revised 8 October 2008, Available online 7 December 2008.
论文官网地址:https://doi.org/10.1016/j.cam.2008.12.002