A Weighted Sequential Splitting Method for the 3D Maxwell’s Equations

Vrushali A. Bokil, Puttha Sakkaplangkul (Oregon State University)

We present the Weighted Sequential Splitting (WSS) finite difference time-domain method for Maxwell’s equation in three dimensions. In one time step, the WSS scheme consists of several substages each of which involves the solutions of a 1D Maxwell system. At the end of a time step we take a weighted average of solutions of different substages with a weight parameter θ, 0 ≤ θ ≤ 1. We prove that the WSS scheme is an unconditionally stable scheme and the order of accuracy is of the first order in time when θ = 0.5 and of the second order when θ = 0.5. We prove the convergence of the method for all values of the weight parameter θ and provide error estimates. Furthermore, numerical experiments will be presented that illustrate our theoretical results.