Volume 6, Issue 2
Development of a $hp$-Like Discontinuous Galerkin Time-Domain Method on Non-Conforming Simplicial Meshes for Electromagnetic Wave Propagation

Int. J. Numer. Anal. Mod., 6 (2009), pp. 193-216.

Published online: 2009-06

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• Abstract

This work is concerned with the design of a $hp$-like discontinuous Galerkin (DG) method for solving the two-dimensional time-domain Maxwell equations on non-conforming locally refined triangular meshes. The proposed DG method allows non-conforming meshes with arbitrary-level hanging nodes. This method combines a centered approximation for the evaluation of fluxes at the interface between neighboring elements of the mesh, with a leap-frog time integration scheme. It is an extension of the DG formulation recently studied in [13]. Several numerical results are presented to illustrate the efficiency and the accuracy of the method, but also to discuss its limitations, through a set of 2D propagation problems in homogeneous and heterogeneous media.

• Keywords

Maxwell's equations, discontinuous Galerkin method, $hp$-like method, non-conforming triangular mesh, computational electromagnetism.

65M50 65M60 78A25 78A45

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@Article{IJNAM-6-193, author = {}, title = {Development of a $hp$-Like Discontinuous Galerkin Time-Domain Method on Non-Conforming Simplicial Meshes for Electromagnetic Wave Propagation}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2009}, volume = {6}, number = {2}, pages = {193--216}, abstract = {

This work is concerned with the design of a $hp$-like discontinuous Galerkin (DG) method for solving the two-dimensional time-domain Maxwell equations on non-conforming locally refined triangular meshes. The proposed DG method allows non-conforming meshes with arbitrary-level hanging nodes. This method combines a centered approximation for the evaluation of fluxes at the interface between neighboring elements of the mesh, with a leap-frog time integration scheme. It is an extension of the DG formulation recently studied in [13]. Several numerical results are presented to illustrate the efficiency and the accuracy of the method, but also to discuss its limitations, through a set of 2D propagation problems in homogeneous and heterogeneous media.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/763.html} }
TY - JOUR T1 - Development of a $hp$-Like Discontinuous Galerkin Time-Domain Method on Non-Conforming Simplicial Meshes for Electromagnetic Wave Propagation JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 193 EP - 216 PY - 2009 DA - 2009/06 SN - 6 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/763.html KW - Maxwell's equations, discontinuous Galerkin method, $hp$-like method, non-conforming triangular mesh, computational electromagnetism. AB -

This work is concerned with the design of a $hp$-like discontinuous Galerkin (DG) method for solving the two-dimensional time-domain Maxwell equations on non-conforming locally refined triangular meshes. The proposed DG method allows non-conforming meshes with arbitrary-level hanging nodes. This method combines a centered approximation for the evaluation of fluxes at the interface between neighboring elements of the mesh, with a leap-frog time integration scheme. It is an extension of the DG formulation recently studied in [13]. Several numerical results are presented to illustrate the efficiency and the accuracy of the method, but also to discuss its limitations, through a set of 2D propagation problems in homogeneous and heterogeneous media.

H. Fahs. (1970). Development of a $hp$-Like Discontinuous Galerkin Time-Domain Method on Non-Conforming Simplicial Meshes for Electromagnetic Wave Propagation. International Journal of Numerical Analysis and Modeling. 6 (2). 193-216. doi:
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