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Volume 31, Issue 2
A Multi-Domain Spectral IPDG Method for Helmholtz Equation with High Wave Number

Lunji Song, Jing Zhang & Li-Lian Wang

DOI: 10.4208/jcm.1210-m4094

J. Comp. Math., 31 (2013), pp. 107-136.

Published online: 2013-04

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  • 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.  

  • Keywords

Helmholtz equation, High wavenumber, Global DtN boundary condition, IPDG, Multli-domain spectral method.

  • AMS Subject Headings

65N35, 65E05, 65M70, 41A05, 41A10, 41A25.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-31-107, author = {Lunji Song, Jing Zhang and Li-Lian Wang}, title = {A Multi-Domain Spectral IPDG Method for Helmholtz Equation with High Wave Number}, journal = {Journal of Computational Mathematics}, year = {2013}, volume = {31}, number = {2}, pages = {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.  

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1210-m4094}, url = {http://global-sci.org/intro/article_detail/jcm/9725.html} }
TY - JOUR T1 - A Multi-Domain Spectral IPDG Method for Helmholtz Equation with High Wave Number AU - Lunji Song, Jing Zhang & Li-Lian Wang JO - Journal of Computational Mathematics VL - 2 SP - 107 EP - 136 PY - 2013 DA - 2013/04 SN - 31 DO - http://doi.org/10.4208/jcm.1210-m4094 UR - https://global-sci.org/intro/article_detail/jcm/9725.html KW - Helmholtz equation, High wavenumber, Global DtN boundary condition, IPDG, Multli-domain spectral method. AB -

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.  

Lunji Song, Jing Zhang and Li-Lian Wang. (2013). A Multi-Domain Spectral IPDG Method for Helmholtz Equation with High Wave Number. Journal of Computational Mathematics. 31 (2). 107-136. doi:10.4208/jcm.1210-m4094
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