Method of Moments: A General Framework for Frequency- and Time-domain Numerical Methods

Many numerical methods have been derived and developed in the past five decades for solving electromagnetic structure problems. They can be categorized into frequency- and time-domain methods. Among them are frequency- and time-domain spectral domain methods, finite- difference based methods, finite element FEM methods and integral equation methods. These methods have been studied extensively and become mature enough such that a number of software packages based on them have been developed commercially. However, all these methods appear to have been unrelated and formulated on different mathematical bases. In this paper, we show that all these methods can be derived directly with the Method of Moments (MoM). The differences among them are (1) the equations and quantities to be solved and (2) the expansion and weighting functions used. The work presented here opens a new horizon for developing other new methods under a unifying framework of MoM without considering which methods they belong to.