A Convolution-Free Finite-Element Time-Domain Method for the Nonlinear Dispersive Vector Wave Equation

In this article, a finite-element time-domain method is presented for the solution of the second-order vector wave equation (VWE) subject to electrically complex materials, including general combinations of linear dispersion, instantaneous nonlinearity, and dispersive nonlinearity. The presented method is novel in that it offers greater geometric flexibility than existing finite-difference methods, incorporates both instantaneous and dispersive nonlinearity, scales to arbitrary dispersive and nonlinear orders, and is simpler, faster, and requires less computational complexity than existing mixed formulations due to the use of edge elements only.