TY - JOUR T1 - Development of a $hp$-Like Discontinuous Galerkin Time-Domain Method on Non-Conforming Simplicial Meshes for Electromagnetic Wave Propagation AU - H. Fahs 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.