A second-order space-time accurate scheme for Maxwell's equations in a Cole-Cole dispersive medium

A fully implicit finite-difference time-domain (FDTD) scheme with second-order space-time accuracy for Maxwell's equations in a Cole-Cole dispersive medium is proposed and analyzed. The temporal discretization is built upon Crank-Nicolson method, and the Caputo derivative term is based on the recently established L2-1(sigma) formula and a weighted approach. A rigorous analysis is carried out to show that the proposed scheme is unconditionally stable and has second-order accuracy in both time and space. 2D and 3D numerical examples are presented to validate our theoretical findings.

Automated summary

A fully implicit finite-difference time-domain (FDTD) scheme with second-order space-time accuracy for Maxwell's equations in a Cole-Cole dispersive medium is proposed and analyzed. The proposed scheme is rigorously analyzed and shown to be unconditionally stable with second-order accuracy in both time and space. Numerical examples are provided to validate the theoretical findings.