Computational efficiency of Fang's fourth-order FDTD schemes

Fang 's fourth-order finite-difference time-domain (FDTD) schemes are compared with conventional second-order Yee's FDTD scheme in terms of computational efficiency. A three-dimensional (3D) rectangular cavity partially filled with a dielectric material is considered for the numerical experiments. A set of numerical boundary conditions, constructed consistently with the higher order accuracy of the schemes, enables a realistic assessment of the computational efficiencies of Fang's (4,4) and (2,4) schemes in the presence of metallic and dielectric boundaries. Numerical results show that both Fang's (4,4) and (2,4) schemes are more efficient than Yee's (2,2) scheme by more than two orders of magnitude in CPU time for a fixed error level in the L₂ norm. This comparative study verifies that Fang's explicit fourth-order FDTD methods, complemented with the proposed numerical boundary conditions at planar material interfaces, yield very accurate and computationally very efficient time-domain solvers for the numerical simulation of electromagnetic interactions in three-dimensional multimaterial structures.