ABSTRACT
In solving problems arising from mathematical physics and engineering, we find that it is often possible to replace the problem of integrating a differential equation by the equivalent problem of seeking a function that gives a minimum value of some integral. Problems of this type are called variational problems. The variational methods form a common base for both the method of moments (MoM) and finite element method (FEM). Variational methods can be classified into two groups: direct and indirect methods. The literature on the theory and applications of variational methods to electromagnetics (EM) problems is quite extensive, and no attempt will be made to provide an exhaustive list of references. The variational solution of a given partial differential equation (PDE) using an indirect method usually involves two basic steps: casting the PDE into variational form, and determining the approximate solution using one of the methods.
