An efficient three-dimensional demagnetizing field calculation scheme (abstract)

Abstract

We present an efficient three-dimensional demagnetizing field calculation scheme for micromagnetic simulations of the domain walls in garnet-like materials. We take advantage of the fact that the domain wall is nearly planar and distribute computational power nonuniformly between the bulk of the material and the wall regions. We use fast Fourier convolutions along one dimension (approximately parallel to the domain wall) and a two-dimensional variant of Greengard’s adaptive fast multipole method in the other dimensions. Even a 2D nonadaptive multipole method has the time complexity of the order of N, for N points in contrast to full Fourier convolution (Nlog N) or direct methods (N2). The adaptive method is based on maintaining a point-to-point error bound which allows us to work at high resolution in the region of the domain wall and coarser resolution in the bulk material. In this case, the calculation scales proportional to the domain wall size rather than the sample volume. The error bound calculation is important for our method and it depends on the Gegenbauer’s addition theorem for the modified Bessel functions. Due to the complex nature of this addition theorem, we have relied on numerical methods, comparing our method to the direct calculations for small size samples. We have implemented this scheme on an SGI workstation and we are reporting the outcome of the 2D adaptive fast multipole method implementation. We have studied the relationship between error bounds, domain wall size, and actual time. We have also compared our results with that of M. Redjdal’s method.