Marching on in anything : Solving electromagnetic field equations with a varying physical parameter

Abstract

In this paper, we consider the determination of electromagnetic flelds for a (large) number of values of a physical parameter. We restrict ourselves to the case where the linear system originates from one or more integral equations. we apply an iterative procedure based on the minimization of an integrated squared error, and start this procedure from an initial estimate that is a linear combination of the last few "final" ræults. When the coefficients in this extrapolation is determined by minimizing the integrated squared error for the actual value of the parameter, the built-in orthogonality in this type of scheme ensures that only a few iteration steps are required to obtain the solution