A dispersion analysis for the finite-element method in time domain with triangular edge elements

Abstract

A numerical dispersion analysis for the finite-element (FE) method in time domain (TD) is presented. The dispersion relation is analitically derived by considering a time-harmonic plane wave propagating through an infinite uniform mesh consisting of equilateral triangular elements. The effect of the time step on the numerical dispersion is investigated and it is shown that, if linear tangential-linear normal (LT-LN) edge-basis functions are used, there exists a time-step value that minimizes the deviation of the dispersion relation from the ideal linear case. In particular, the analysis performed shows that this optimum time step holds for any propagation direction of the plane wave within the mesh and, virtually, for any frequency, strongly enhancing numerical accuracy of the FE-TD method. As a working example, we choose to compare the numerically computed TE modes of two-dimensional guiding structures with the corresponding analytical values; to this end, an efficient procedure for the computation of the eigenfrequencies is proposed, allowing us to avoid TD data processing.