The Method of Weighted Residuals: A General Approach to Deriving Time- and Frequency-Domain Numerical Methods

The Method of the Weighted Residuals (MWR), sometimes known as the Method of Moments (MoM), has traditionally been applied in the frequency domain and has been shown to be effective and efficient, especially in computing open electromagnetic structure problems. Although it has been extended to the time domain in various forms, it is generally employed to solve integral formulations derived from Maxwell's equations. Therefore, it is often considered to be one type of numerical method that is different from other numerical methods, such as finite-difference methods. However, in this paper we will show that the MWR, or MoM, is not just a method per se: it can in fact be a general framework for or approach to unifying or deriving most of the numerical methods developed so far, either in the frequency domain or in the time domain. As a result, all numerical methods can be quite easily understood and can be categorized in one general method, although their conventional derivations may still have their respective advantages. One potential application is that the hybridization of different numerical methods can now be done within a uniform framework. The paper is intended for both beginners and experienced practitioners in the area of numerical electromagnetic modeling.