A fast numerical method for a natural boundary integral equation for the Helmholtz equation

Authors:
Song-Hua Li;Ming-Bao Sun
Affiliations:
Department of Mathematics, Hunan Institute of Science and Technology, Yueyang Hunan 414006, PR China;Department of Mathematics, Hunan Institute of Science and Technology, Yueyang Hunan 414006, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

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.