Spatial Reconstruction of Exchange Field Interactions With a Finite Difference Scheme Based on Unstructured Meshes

A finite difference scheme suitable for unstructured meshes is here applied to the spatial reconstruction of the exchange field in Landau-Lifshitz-Gilbert equation. This method determines second-order derivatives by solving a over-determined set of linear equations through norm minimization of a Taylor series expansion functional. In this way, the local character of the exchange field computation typical of standard finite difference schemes is preserved, but similarly to finite element schemes irregular meshes can be handled. In this paper, the accuracy and computational efficiency of the proposed approach is tested in comparison with finite element and structured mesh based finite difference schemes.