Exchange energy formulations for 3D micromagnetics

Exchange energy is especially sensitive to the numerical representation selected. We compare three discretized exchange energy formulations for 3D numerical micromagnetics on rectangular grids. Explicit formulae are provided for both Neumann and Dirichlet boundary conditions. Results illustrate the convergence order of these methods as a function of discretization cell size and the effect of cell size on vortex pinning. Published by Elsevier B.V.