M. Min, "Disctoninuous Galerkin Method Based on Quadrilateral Mesh for Maxwell's Equations," Preprint ANL/MCS-P1233-0205, February 2005. [pdf]
Discontinuous Galerkin (DG) method based on quadrilateral spectral element discretizations are applied to the electromagnetic wave time-domain simulations in free space. The 2D Maxwell's equations in transverse-magnetic mode are described in conservation form. Numerical flux is used for the communication at the interface between elements and boundary condition. Computational results on the field distribution are demonstrated, including h- and p-convergence in maximum norm with this method. This work is our first step toward two- and three-dimensional nanophotonic simulations using this higher order method.