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 *
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DOI：
10.4208/jcm.1210-m4094
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发表时间：
2013-03
影响因子：
0.9
通讯作者：
Lunji Song;Jing Zhang;Lilian Wang
中科院分区：
文献类型：
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作者：
Lunji Song;Jing Zhang;Lilian Wang
本文研究了一种基于内罚间断Galerkin（IPDG）格式的多区域谱方法，该方法用于求解外Helmholtz问题的精确圆形或球形Dirichlet-to-Neumann（DtN）边界条件.提出了一种有效的迭代方法来局部化全局DtN边界条件，这有利于多域方法的实现，以及对复杂几何形状的散射体的处理。在不连续Galerkin公式下，该方法允许在不同子域上使用不同次数的多项式基函数，更重要的是，可以得到谱格式的显式波数依赖估计，这在多域连续Galerkin公式下是不可能的.
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.