Finite Element Technique for Solving the Two-Dimensional Maxwell's Equations in the Time Domain

摘要

In this paper, we present a two-dimensional Galerkin finite element formulation of the Maxwell's equations in the time domain. The Galerkin element integrals are computed analytically and an explicit forward-backward time integration scheme is employed for advancing the resulting set of ordinary differential equations in time. We will compare two formulations of the simple 4-node bilinear element: an equal-order interpolation element in which both the electric field and the magnetic field are approximated by bilinear basis functions; and a mixed-interpolation element in which the electric field is approximated as piecewise constant and the magnetic field as piecewise bilinear functions. The mixed formulation may be viewed as a finite element analog to certain staggered finite difference representations. Numerical examples will be presented to evaluate the accuracy of these two elements. 5 refs., 3 figs. (ERA citation 13:052802)