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We propose high-order FDTD schemes based on the Correction Function Method(CFM) for Maxwell's interface problems with discontinuous coefficients andcomplex interfaces. The key idea of the CFM is to model the correction functionnear an interface to retain the order of a finite difference approximation. Forthis, we solve a system of PDEs based on the original problem by minimizing anenergy functional. The CFM is applied to the standard Yee scheme and afourth-order FDTD scheme. The proposed CFM-FDTD schemes are verified in 2-Dusing the transverse magnetic mode (TM$_z$). Numerical examples includescattering of magnetic and non-magnetic dielectric cylinders, and problems withmanufactured solutions using various complex interfaces and discontinuouspiecewise varying coefficients. Long-time simulations are also performed toprovide numerical evidences of the stability of the proposed numericalapproach. The proposed CFM-FDTD schemes achieve up to fourth-order convergencein $L^2$-norm and provide approximations devoid of spurious oscillations.

journal of scientific computing

High-order FDTD schemes for Maxwell's interface problems with  discontinuous coefficients and complex interfaces based on the Correction  Function Method