Exchange energy representations in computational micromagnetics

In order to solve Brown's equations, which describe a continuous medium, computational micromagnetic modeling requires a discrete representation of the magnetization M(r), and a discrete representation of the derivatives of M(r) must be chosen. This choice may be made through an explicit choice of interpolation or through the choice of numerical representation of Brown's equations. In this paper we describe some alternative representations of the exchange energy on a square 2-D grid, and test these representations through comparison with analytical results for magnetization spirals and with simulations testing vortex and domain wall mobility.