MODERN KRYLOV SUBSPACE METHODS IN ELECTROMAGNETIC FIELD COMPUTATION USING THE FINITE INTEGRATION THEORY

Abstract

A theoretical basis for numerical electromagnetics, the so-called Finite Integration Theory, is described. Based upon Maxwell's equations in their integral form, it results in a set of matrix equations, each of which is a discrete analogue of its original analytical equation. Applications of this discretization process are described here in the context of the numerical simulation of electroquasistatic problems and of time-harmonic field computations including a new type of waveguide boundary condition, which is presented here for the first time. In both fields the process of mathematical modelling and discretization yields large systems of complex linear equations which have to be solved numerically. For this task several modern Krylov subspace methods are presented such as BiCG, CGS and their more recent stabilized variants CGS2, BiCGSTAB(I) and TFQMR. They are applied in connection with efficient preconditioning methods. The applicability of these modern methods is shown for a number of examples for both problem types. [Vol. 11, No. 1 (1996), pp 70-84, Special issue on Applied Mathematics: Meeting the challenges presented by computational electromagnetics]