Applications of H-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 P. 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 P is numerically the most challenging issue, as it leads to densely populated matrices. We show how an efficient treatment of both P and the corresponding bilinear form can be achieved by application of H-matrix techniques.
micromagnetics landau-lifshitz model magnetic potential finite element method hierarchical matrices interpolation