High-Order FDTD Schemes for Maxwell's Interface Problems with Discontinuous Coefficients and Complex Interfaces Based on the Correction Function Method

We propose high-order FDTD schemes based on the Correction Function Method (CFM) (Marques et al. in J Comput Phys 230:7567-7597, 2011) for Maxwell's interface problems with discontinuous coefficients and complex interfaces. The key idea of the CFM is to model the correction function near an interface to retain the order of a finite difference approximation. To do so, we solve a system of PDEs based on the original problem by minimizing an energy functional. The CFM is applied to the standard Yee scheme and a fourth-order FDTD scheme. The proposed CFM-FDTD schemes are verified in 2-D using the transverse magnetic (TMz) mode. Numerical examples include scattering of magnetic and non-magnetic dielectrics, and problems with manufactured solutions using various complex interfaces and discontinuous piecewise varying coefficients. Long-time simulations are also performed to investigate the stability of CFM-FDTD schemes. The proposed CFM-FDTD schemes achieve up to fourth-order convergence in L-2-norm and provide approximations devoid of spurious oscillations.

Automated summary

This paper proposes high-order FDTD schemes for solving Maxwell's interface problems with discontinuous coefficients and complex interfaces, based on the Correction Function Method (CFM). The CFM is used to model the correction function near the interface and retain the accuracy of finite difference approximation. The proposed CFM-FDTD schemes achieve fourth-order convergence and provide accurate solutions devoid of spurious oscillations.