Implicit ID-FDTD Algorithm Based on Crank-Nicolson Scheme: Dispersion Relation and Stability Analysis

A new implicit isotropic-dispersion finite difference time domain (ID-FDTD) algorithm is proposed, which is formulated based on the Crank-Nicolson (CN) implicit scheme. The update equation of the new scheme is given for a three dimension (3D) problem and a general lossy medium including electric and magnetic losses. The dispersion relation of the CN ID-FDTD scheme is obtained based on the eigen-analysis technique. Also, the unconditional stability is mathematically proved by using the energy method. For a practical application, a maximum time-limit is proposed for free space. To validate the proposed scheme, a 2D cavity problem is considered. The electric fields inside the cavity, which are calculated by the proposed, conventional CN FDTD schemes, and the exact solution, are compared.