Calculation of magnetostatic fields is usually the most time-consuming stage of micromagnetic simulations. In this article, the Bramble-Pasciak-Xu multilevel preconditioners (MP) are applied to the computation of magnetostatic fields in media such as magnetic tapes or thin films. The asymptotic number of arithmetic operations is optimal and proportional to the number of nodes in the finite element mesh. Unlike the fast Fourier transform, MP are applicable to irregular meshes. Local (adaptive) mesh refinement can be implemented by switching to the hierarchical basis.
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Tsukerman et al. (1998) studied this question.
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