  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.
