An Efficient 2D ADI-FDTD Modeling of High-Order, Frequency-Dependent Media

The alternating-direction implicit finite-difference time-domain (ADI-FDTD) method is extended for modeling the propagation of transverse-electric waves in high-order, frequency-dependent media. Ohm´s law is considered as the constitutive relation with the complex conductivity assumed to be a high-order rational function of the frequency. Contrary to previously reported approaches, the integration of the constitutive relation over a full time-step is not split into several substeps, which improves the computational efficiency of the resulting algorithm. In addition, the numerical dispersion relation is derived in a closed form. To illustrate the validity and accuracy of the formulation, we consider a muscle model that consists of a static conductivity and three Debye poles.