A Multi-Domain Spectral IPDG Method for Helmholtz Equation with High Wave Number

A Multi-Domain Spectral IPDG Method for Helmholtz Equation with High Wave Number

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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