Applications of [inline-graphic not available: see fulltext]-Matrix Techniques in Micromagnetics

The variational model by Landau and Lifshitz is frequently used in the simulation of stationary micromagnetic phenomena. We consider the limit case of large and soft magnetic bodies, treating the associated Maxwell equation exactly via an integral operator [inline-graphic not available: see fulltext]. In numerical simulations of the resulting minimization problem, difficulties arise due to the imposed side-constraint and the unboundedness of the domain. We introduce a possible discretization by a penalization strategy. Here the computation of [inline-graphic not available: see fulltext] is numerically the most challenging issue, as it leads to densely populated matrices. We show how an efficient treatment of both [inline-graphic not available: see fulltext] and the corresponding bilinear form can be achieved by application of [inline-graphic not available: see fulltext]-matrix techniques.