A survey of various numerical techniques to solve operator equations in electromagnetics

The objective of this paper is to survey many of the popular methods utilized in solving numerical problems arising in electromagnetics. Historically, the matrix methods have been quite popular. One of the primary objectives of this paper is to introduce a new class of iterative methods, which have advantages over the classical matrix methods in the sense that a given problem may be solved to a prespecified degree of accuracy. Also, these iterative methods (particularly conjugate gradient methods) converge to the solution in a finite number of steps irrespective of the initial starting guess. Numerical examples have been presented to illustrate the principles.