Computation of Demagnetization Tensors by Utilizing Fourier Properties

We describe a method for the computation of the discrete demagnetization tensor on regular cuboid grids. Assuming homogeneously magnetized cells, the tensor components can be calculated exactly by known analytical formulas. These integral-based expressions can be expensive due to their nested nature and difficult to code. The novelty of this paper is that parts of the tensor computation are moved to Fourier space, which simplifies the implementation. The main idea is that some nested sums, required for the computation of the tensor in real space, are replaced by simple multiplications with real factors in Fourier space. For regular grids, the demagnetization field is usually computed in Fourier space by application of the convolution theorem. Thus, computing the tensor in Fourier space in the first place does not introduce any drawbacks.