Iterative Methods for the Saddle-Point Problem Arising from the HC /EI Formulation of the Eddy Current Problem

This paper is concerned with the resolution of the linear system arising from a finite element approximation of the time-harmonic eddy current problem. We consider the HC/EI formulation introduced and analyzed in [2], where an optimal error estimate for the finite element approximation using edge elements of the first order is proved. We reduce the linear system by eliminating the Lagrange multiplier introduced in the insulator region. Two different iterative procedures are proposed: a modified SOR method and an Uzawa-like method. The finite element scheme has been implemented in Matlab and the two iterative procedures have been compared by solving four different test problems.