A MULTI-DOMAIN SPECTRAL IPDG METHOD FOR HELMHOLTZ EQUATION WITH HIGH WAVE NUMBER  

作　　者：Lunji Song Jing Zhang Li-Lian Wang 

机构地区：[1]School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China [2]School of Mathematics and Statistics, Huazhong Normal University, Wuhan ~300~9, China [3]Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore

出　　处：《Journal of Computational Mathematics》2013年第2期107-136,共30页计算数学（英文）

基　　金：The work of the first author was partially supported by the National Natural Science Foundation of China （11026065 and 11101196）. This work was largely done when this author worked as a Research Fellow in Nanyang Technological University. The work of the second author was supported by the National Natural Science Foundation of China （11201166）. The work of the third author was supported by Singapore MOE Tier 1 Grant （2013-2016）, and Singapore A＊STAR-SERC-PSF Grant 122-PSF-0007.

摘　　要：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 con- dition. An effective iterative approach is proposed to localize the global DtN boundary condition, which facilitates the implementation of multi-domain methods, and the treat- ment for complex geometry of the scatterers. Under a discontinuous Galerkin formulation, the proposed method allows to use polynomial basis functions of different degree on dif- ferent 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.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 con- dition. An effective iterative approach is proposed to localize the global DtN boundary condition, which facilitates the implementation of multi-domain methods, and the treat- ment for complex geometry of the scatterers. Under a discontinuous Galerkin formulation, the proposed method allows to use polynomial basis functions of different degree on dif- ferent 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.

关 键 词：Helmholtz equation High wavenumber Global DtN boundary condition IPDG Multli-domain spectral method. 

分 类 号：O241.82[理学—计算数学] O562.3[理学—数学]