Year: 2013
Journal of Computational Mathematics, Vol. 31 (2013), Iss. 2 : pp. 107–136
Abstract
This paper is concerned with a multi-domain spectral method, based on an interior penalty discontinuous Galerkin (IPDG) formulation, for the exterior Helmholtz problem truncated via an exact circular or spherical Dirichlet-to-Neumann (DtN) boundary condition. An effective iterative approach is proposed to localize the global DtN boundary condition, which facilitates the implementation of multi-domain methods, and the treatment for complex geometry of the scatterers. Under a discontinuous Galerkin formulation, the proposed method allows to use polynomial basis functions of different degree on different subdomains, and more importantly, explicit wave number dependence estimates of the spectral scheme can be derived, which is somehow implausible for a multi-domain continuous Galerkin formulation.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1210-m4094
Journal of Computational Mathematics, Vol. 31 (2013), Iss. 2 : pp. 107–136
Published online: 2013-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 30
Keywords: Helmholtz equation High wavenumber Global DtN boundary condition IPDG Multli-domain spectral method.
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