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Volume 25, Issue 5
Error Analysis of the Plane Wave Discontinuous Galerkin Method for Maxwell's Equations in Anisotropic Media

Long Yuan & Qiya Hu

DOI: 10.4208/cicp.OA-2018-0104

Commun. Comput. Phys., 25 (2019), pp. 1496-1522.

Published online: 2019-01

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  • Abstract

In this paper we investigate the plane wave discontinuous Galerkin method for three-dimensional anisotropic time-harmonic Maxwell's equations with diagonal matrix coefficients. By introducing suitable transformations, we define new plane wave basis functions and derive error estimates of the approximate solutions generated by the proposed discretization method for the considered homogeneous equations. In the error estimates, some dependence of the error bounds on the condition number of the coefficient matrix is explicitly given. Combined with local spectral element method, we further prove a convergence result for the nonhomogeneous case. Numerical results verify the validity of the theoretical results, and indicate that the resulting approximate solutions generated by the PWDG possess high accuracies.

  • Keywords

Time-harmonic Maxwell's equations, anisotropic media, plane-wave basis, error estimates, nonhomogeneous.

  • AMS Subject Headings

65N30, 65N55

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-25-1496, author = {Long Yuan and Qiya Hu}, title = {Error Analysis of the Plane Wave Discontinuous Galerkin Method for Maxwell's Equations in Anisotropic Media}, journal = {Communications in Computational Physics}, year = {2019}, volume = {25}, number = {5}, pages = {1496--1522}, abstract = {

In this paper we investigate the plane wave discontinuous Galerkin method for three-dimensional anisotropic time-harmonic Maxwell's equations with diagonal matrix coefficients. By introducing suitable transformations, we define new plane wave basis functions and derive error estimates of the approximate solutions generated by the proposed discretization method for the considered homogeneous equations. In the error estimates, some dependence of the error bounds on the condition number of the coefficient matrix is explicitly given. Combined with local spectral element method, we further prove a convergence result for the nonhomogeneous case. Numerical results verify the validity of the theoretical results, and indicate that the resulting approximate solutions generated by the PWDG possess high accuracies.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0104}, url = {http://global-sci.org/intro/article_detail/cicp/12959.html} }
TY - JOUR T1 - Error Analysis of the Plane Wave Discontinuous Galerkin Method for Maxwell's Equations in Anisotropic Media AU - Long Yuan & Qiya Hu JO - Communications in Computational Physics VL - 5 SP - 1496 EP - 1522 PY - 2019 DA - 2019/01 SN - 25 DO - http://doi.org/10.4208/cicp.OA-2018-0104 UR - https://global-sci.org/intro/article_detail/cicp/12959.html KW - Time-harmonic Maxwell's equations, anisotropic media, plane-wave basis, error estimates, nonhomogeneous. AB -

In this paper we investigate the plane wave discontinuous Galerkin method for three-dimensional anisotropic time-harmonic Maxwell's equations with diagonal matrix coefficients. By introducing suitable transformations, we define new plane wave basis functions and derive error estimates of the approximate solutions generated by the proposed discretization method for the considered homogeneous equations. In the error estimates, some dependence of the error bounds on the condition number of the coefficient matrix is explicitly given. Combined with local spectral element method, we further prove a convergence result for the nonhomogeneous case. Numerical results verify the validity of the theoretical results, and indicate that the resulting approximate solutions generated by the PWDG possess high accuracies.

Long Yuan and Qiya Hu. (2019). Error Analysis of the Plane Wave Discontinuous Galerkin Method for Maxwell's Equations in Anisotropic Media. Communications in Computational Physics. 25 (5). 1496-1522. doi:10.4208/cicp.OA-2018-0104
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