Different numerical approaches for the stray-field calculation in the context of micromagnetic simulations are investigated. We compare finite difference based fast Fourier transform methods, tensor grid methods and the finite-element method with shell transformation in terms of computational complexity, storage requirements and accuracy tested on several benchmark problems. These methods can be subdivided into integral methods (fast Fourier transform methods, tensor-grid method) which solve the stray field directly and in differential equation methods (finite-element method), which compute the stray field as the solution of a partial differential equation. It turns out that for cuboid structures the integral methods, which work on cuboid grids (fast Fourier transform methods and tensor grid methods) outperform the finite-element method in terms of the ratio of computational effort to accuracy. Among these three methods the tensor grid method is the fastest. However, the use * of the tensor grid method in the context of full micromagnetic codes is not well investigated yet. The finite-element method performs best for computations on curved structures. Stray-Field ProblemConsider a magnetization configuration M that is defined on a finite region Ω = {r : M (r) = 0}. In order to perform minimization of the full micromagnetic energy functional or solve the Landau-Lifshitz-Gilbert (LLG) equation it is necessary to compute the stray field within the finite region Ω. The stray-field energy is given by(1)

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In micromagnetic simulations, the magnetization in one simulation cell is acted upon by the demagnetization field that is generated by all simulation cells. In simulations with periodic boundary conditions, this leads to an infinite number of interactions that have to be taken into account. A method is presented that allows for an accurate calculation of the demagnetization tensor with one and two-dimensional periodic boundary conditions using a small amount of computation time. The method has been implemented in a micromagnetic simulation tool. For a reasonable accuracy and two-dimensional periodic boundary conditions the presented method is about six orders of magnitude faster than the straightforward method in which all cells beyond a certain distance are neglected.Index Terms-Accurate simulation, demagnetization field, finite difference method, micromagnetic simulator, micromagnetism, periodic boundary conditions.