General magnetostatic shape-shape interactions

The magnetostatic interaction energy between two magnetic elements of arbitrary shape is presented as a convolution between the cross-correlation of the particle shapes and the dipolar tensor field. A generalized dipole-dipole interaction is derived, where the magnetic moments associated with the two particles interact through a magnetometric tensor field, carrying all the shape information. Example computations are given in order to verify the correctness of the formalism. The well-known result of the interaction between prisms, employed in most micromagnetic simulations, is correctly retrieved. The numerical accuracy of the method is also compared to a simple analytical result. Finally, one additional example computation, two interlaced interacting rings, is presented to show the generality of the formalism.