Generalization of the Finite-Difference-Based Time-Domain Methods Using the Method of Moments

Many finite-difference-based time-domain methods have been developed in the past three decades. Typical among them are the finite-difference time-domain method of Yee´s scheme, the transmission-line-matrix method, the multiresolution time-domain method, the pseudospectral time-domain method, and the unconditionally stable finite-difference time-domain methods. All these methods have become powerful tools in solving electromagnetic structure problems, yet their formulations appear to be unrelated. The concept of the method of moments (MoM) is applied in this paper to generalize all these different finite-difference-based methods. It is shown theoretically that differences among various finite-difference-based methods lie in different choices of basis functions used in solution expansions and weighting functions in error testing, in both time and space. The significance of this paper is twofold: 1) all the finite-difference time-domain-based methods can now be unified under the framework of MoM and 2) any other new finite-difference-based time-domain methods, including hybrid techniques, may now be developed with MoM procedure