Splitting finite element methods for time dependent Maxwell's equations in 2D

Abstract

Operator splitting is a new and efficient technique in the recently proposed splitting finite difference time domain methods for the Maxwell's equations in time domain. In this paper we extend this new method to the finite element methods of Maxwell's equations and propose a new kind finite element time domain(FETD) method, called S-FETD method, for the 2D time dependent Maxwell's equations with the perfectly electric conducting boundary condition. It is shown that S-FETD is unconditionally stable and second order accurate in time. By selecting finite elements on rectangles and base functions, the S-FETD schemes can be regarded as two 1D problems and solved practically. Numerical experiments by using linear finite elements to test the new FETD methods are presented and error of the FE solution in L <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> norm is given.