Recent Achievements on a DGTD Method for Time-Domain Electromagnetics

Abstract

Abstract-We report on results concerning a discontinuous Galerkin time domain (DGTD) method for the solution of Maxwell equations. This DGTD method is formulated on unstructured simplicial meshes (triangles in 2D and tetrahedra in 3D). Within each mesh element, the electromagnetic field components are approximated by an arbitrarily high order nodal polynomial while, in the original formulation of the method, time integration is achieved by a second order Leap-Frog scheme. Here, we discuss about several recent developments aiming at improving the accuracy and the computational efficiency of this DGTD method in view of the simulation of problems involving general domains and heterogeneous media.

The use of hybrid meshes to improve the efficiency of a discontinuous Galerkin method for the solution of Maxwell’s equations

“…The development of high-order DG methods for the numerical solution of Maxwell's equations in the time domain has been a particularly active area of research [13,14,15,16,17,18,19,20,21]. As the automatic generation of unstructured hexahedral meshes is still an open problem [22,23], most attention has been directed towards the use of unstructured triangular and tetrahedral meshes, in order that fully automatic mesh generators can be employed.…”