Linear Algebra Methods in a Mixed Approximation of Magnetostatic Problems

Abstract

In the solution of magnetostatic problems the use of a mixed formulation based on both the magnetic and magnetic displacement fields is particularly appropriate as it allows us to impose the physical conditions exactly and to maintain the continuity properties of the two fields, together with an efficient treatment of boundary conditions. The discretization by means of a proper finite element method yields a strongly structured algebraic linear system. This paper is concerned with the solution of this large, very sparse indefinite linear system. In particular, we present the implementation of some known direct and preconditioned iterative methods and discuss their performance on two-dimensional (2-D) and three-dimensional (3-D) specific models. We show that the 2-D system can be efficiently handled by appropriate variants of these schemes, while preliminary tests on the 3-D system give some insight in the understanding of the analysis that needs to be done.