Volume 12, Issue 2
The Plane Wave Discontinuous Galerkin Method Combined with Local Spectral Finite Elements for the Wave Propagation in Anisotropic Media

Long Yuan

Numer. Math. Theor. Meth. Appl., 12 (2019), pp. 517-546.

Published online: 2018-12

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  • Abstract

In this paper we are concerned with plane wave discretizations of nonhomogeneous and anisotropic time-harmonic Maxwell's equations. Combined with local spectral element method, we design a plane wave discontinuous Galerkin method for the discretization of such three dimensional nonhomogeneous and anisotropic Maxwell's equations. The error estimates of the approximation solutions generated by the proposed discretization method are derived in one special case of the TE mode scattering. In the error estimates, some dependence of the error bounds on the condition number of the anisotropic matrix is explicitly given. Numerical results indicate that the resulting approximate solutions generated by the new method possess high accuracy and verify the validity of the theoretical results.

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@Article{NMTMA-12-517, author = {}, title = {The Plane Wave Discontinuous Galerkin Method Combined with Local Spectral Finite Elements for the Wave Propagation in Anisotropic Media}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2018}, volume = {12}, number = {2}, pages = {517--546}, abstract = {

In this paper we are concerned with plane wave discretizations of nonhomogeneous and anisotropic time-harmonic Maxwell's equations. Combined with local spectral element method, we design a plane wave discontinuous Galerkin method for the discretization of such three dimensional nonhomogeneous and anisotropic Maxwell's equations. The error estimates of the approximation solutions generated by the proposed discretization method are derived in one special case of the TE mode scattering. In the error estimates, some dependence of the error bounds on the condition number of the anisotropic matrix is explicitly given. Numerical results indicate that the resulting approximate solutions generated by the new method possess high accuracy and verify the validity of the theoretical results.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2017-0139}, url = {http://global-sci.org/intro/article_detail/nmtma/12907.html} }
TY - JOUR T1 - The Plane Wave Discontinuous Galerkin Method Combined with Local Spectral Finite Elements for the Wave Propagation in Anisotropic Media JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 517 EP - 546 PY - 2018 DA - 2018/12 SN - 12 DO - http://doi.org/10.4208/nmtma.OA-2017-0139 UR - https://global-sci.org/intro/article_detail/nmtma/12907.html KW - AB -

In this paper we are concerned with plane wave discretizations of nonhomogeneous and anisotropic time-harmonic Maxwell's equations. Combined with local spectral element method, we design a plane wave discontinuous Galerkin method for the discretization of such three dimensional nonhomogeneous and anisotropic Maxwell's equations. The error estimates of the approximation solutions generated by the proposed discretization method are derived in one special case of the TE mode scattering. In the error estimates, some dependence of the error bounds on the condition number of the anisotropic matrix is explicitly given. Numerical results indicate that the resulting approximate solutions generated by the new method possess high accuracy and verify the validity of the theoretical results.

Long Yuan. (2020). The Plane Wave Discontinuous Galerkin Method Combined with Local Spectral Finite Elements for the Wave Propagation in Anisotropic Media. Numerical Mathematics: Theory, Methods and Applications. 12 (2). 517-546. doi:10.4208/nmtma.OA-2017-0139
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