Differential material matrices for the finite integration technique

¹ Katholieke Universiteit Leuven, Campus Kortrijk, Etienne Sabbelaan 53, 8500 Kortrijk, Belgium
² Computer Simulation Technology, Bad Nauheimer Straße 19, 64289 Darmstadt, Germany
³ Institut für Theorie Elektromagnetischer Felder, Technische Universität Darmstadt, Schloßgartenstraße 8, 64289 Darmstadt, Germany

Corresponding author: herbert.degersem@kuleuven-kortrijk.be

Received: 18 January 2007
Accepted: 21 June 2007
Published online: 16 August 2007

Abstract

In this paper, differential conductivity and reluctivity matrices are constructed for formulations discretised by the finite integration technique and linearised by the Newton method. It turns out that these matrices are nondiagonal and unsymmetric, even in the case that orthogonal grids are used. A diagonal approximation of the differential matrices leads to an approximate Newton method where cross-magnetisation effects are no longer considered, except in the update between the successive nonlinear iteration steps. The approximate method does not guarantee second order convergence but outperforms the true Newton method when only a moderate accuracy is required.