Finite element time domain method using Laguerre polynomials

In this work, we present a numerical method to obtain an unconditionally stable solution for the finite element method in time domain (FETD) for two-dimensional TE_z case. Our method does not utilize the customary marching-on in time solution method often used to solve a hyperbolic partial differential equation. Instead we solve the time domain wave equation by expressing the transient behaviors in terms of weighted Laguerre polynomials. By using these causal orthonormal basis functions for the temporal variation, the time derivatives can be handled analytically. To verify our method, we apply it to two-dimensional parallel plate waveguide and compare the result to that of the conventional FETD using the Newmark-Beta method.