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 - <p style="text-align: justify;">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. &nbsp;</p>