Dispersion analysis of triangle-based Whitney element methods for electromagnetic wave propagation

Abstract

We study the numerical dispersion/dissipation of a triangle-based edge Finite Element Method (edgeFEM) of degree r ≥ 1 when coupled with the Leap-Frog (LF) finite difference scheme to simulate the electromagnetic wave propagation over a structured triangulation of the 2D physical domain. The analysis addresses the discrete eigenvalue problem resulting from the approximation of the dispersion relation. First, we present semi-discrete dispersion graphs by varying the approximation degree r and the number of discrete points per wavelength. The fully-discrete ones are then obtained by varying also the time step. Numerical results for the edgeFEM, resp. edgeFEM-LF, are compared with those for the node Finite Element Method (nodeFEM), resp. nodeFEM-LF, applied to the considered problem.