Direct exchange calculation for unstructured micromagnetic meshes

In micromagnetic simulations it is necessary to compute the effective field associated exchange interaction, which corresponds applying Laplace operator magnetization field. The most widely used approach for computing apply finite-difference schemes homogeneous Cartesian meshes. many situations would be computationally advantageous perform simulation on inhomogeneous meshes, but doing so presents a challenge with regard calculation of Here we present construction an method A novel second order differential introduced and applied series analytical functions irregular meshes compared existing methods, finding accuracy improvement up 81% relative finite difference method. then in combination MagTense framework tested μmag standard micromagnetics problems 3 4. find that especially tetrahedral proposed results much faster convergence as function mesh size. We demonstrate converges stably even where some elements have volume small 1/8 base resolution. Finally, show works equally well spatially varying material parameters.