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In this paper we present a method to accurately compute the energy of themagnetostatic interaction between linearly (or uniformly, as a special case)magnetized polyhedrons. The method has applications in finite elementmicromagnetics, or more generally in computing the magnetostatic interactionwhen the magnetization is represented using the finite element method (FEM).  The magnetostatic energy is described by a six-fold integral that is singularwhen the interaction regions overlap, making direct numerical evaluationproblematic. To resolve the singularity, we evaluate four of the six iteratedintegrals analytically resulting in a 2d integral over the surface of apolyhedron, which is nonsingular and can be integrated numerically. Thisprovides a more accurate and efficient way of computing the magnetostaticenergy integral compared to existing approaches.  The method was developed to facilitate the evaluation of the demagnetizinginteraction between neighouring elements in finite-element micromagnetics andprovides a possibility to compute the demagnetizing field using efficient fastmultipole or tree code algorithms.

Computation of the magnetostatic interaction between linearly magnetized polyhedrons