Nonreflecting boundary condition for the wave equation

Authors:
Usaf E. Aladl;A. S. Deakin;H. Rasmussen
Affiliations:
Department of Applied Mathematics, University of Western Ontario, London, Ont., Canada;Department of Applied Mathematics, University of Western Ontario, London, Ont., Canada;Department of Applied Mathematics, University of Western Ontario, London, Ont., Canada
Venue:
Journal of Computational and Applied Mathematics
Year:
2002

Citing 4
Cited 1

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Abstract

To solve the time-dependent wave equation in an infinite two (three) dimensional domain a circular (spherical) artificial boundary is introduced to restrict tile computational domain. To determine the nonreflecting boundary we solve the exterior Dirichlet problem which involves the inverse Fourier transform. The truncation of the continued fraction representation of the ratio of Hankel function, that appear in the inverse Fourier transform, provides a stable and numerically accurate approximation. Consequently, there is a sequence of boundary conditions in both two and three dimensions that are new. Furthermore, only the first derivatives in space and time appear and the coefficients are updated in a simple way from the previous time step. The accuracy of the boundary conditions is illustrated using a point source and the finite difference solution to a Dirichlet problem.