3-D Accurate and Efficient Dispersive Alternating-Direction-Implicit Finite-Difference Time-Domain Algorithm

Abstract

Efficient unconditionally stable finite-difference time-domain (FDTD) method is developed for the electromagnetic (EM) analysis of dispersive media. Toward this purpose, a quadratic complex rational function (QCRF) dispersion model is applied to the alternating-direction-implicit (ADI)-FDTD method. The 3-D update equations of QCRF-ADI-FDTD are derived using Maxwell’s curl equations and the constitutive relation. The periodic boundary condition (PBC) and complex frequency-shifted (CFS) perfectly matched layer (PML) of QCRF-ADI-FDTD is discussed in detail. A 3-D numerical example shows that the time-step size can be increased by the proposed QCRF-ADI-FDTD beyond the Courant-Friedrich-Levy (CFL) number, without numerical instability. As a result, the computational efficiency of QCRF-ADI-FDTD is greatly improved, compared to the conventional QCRF-FDTD.