Numerical analysis of Finite-Difference Time-Domain method for 2D/3D Maxwell's equations in a Cole-Cole dispersive medium.

Two efficient numerical schemes based on L 1 formula and Finite-Difference Time-Domain (FDTD) method are constructed for Maxwell's equations in a Cole-Cole dispersive medium. The temporal discretizations are built upon the leap-frog method and Crank-Nicolson method, respectively. We carry out the energy stability and error analysis rigorously by the energy method. Both schemes have been proved convergence with order O ((Δ t) 2 − α + (Δ x) 2 + (Δ y) 2) , where Δ t , Δ x , Δ y are respectively the step sizes in time, space in x- and y-direction. The parameter α is a measure of the dispersion broadening. Numerical experiments are performed to confirm our theoretical analysis. [ABSTRACT FROM AUTHOR]