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