FDTD schemes for Maxwell's equations with embedded perfect electric conductors based on the correction function method

Abstract

In this work, we propose FDTD schemes based on the correction function method (CFM) to discretize Maxwell's equations with interface conditions. We focus on problems involving various geometries of the interface and perfect electric conductors for which the surface current and charge density are either known or unknown. To fulfill the lack of information on the interface when the surface current and charge density are unknown, we propose the use of fictitious interface conditions. The minimization problem needed for CFM approaches is analyzed and well-posed under reasonable assumptions. The consistency and stability analysis are also performed on the proposed CFM-FDTD schemes. Numerical experiments in 2-D have shown that CFM-FDTD schemes can achieve high-order convergence, that is third and fourth order convergence in respectively L ∞ and L 1 norm, for problems involving a PEC and various geometries of the interface. However, the condition number of the matrix coming from the minimization problem increases with the order of CFM-FDTD schemes.