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We present a steepest descent energy minimization scheme for micromagnetics.The method searches on a curve that lies on the sphere which keeps themagnitude of the magnetization vector constant. The step size is selectedaccording to a modified Barzilai-Borwein method. Standard linear tetrahedralfinite elements are used for space discretization. For the computation ofstatic hysteresis loops the steepest descent minimizer is faster than aLandau-Lifshitz micromagnetic solver by more than a factor of two. The speed upon a graphic processor is 4.8 as compared to the fastest single-core CPUimplementation.

LaBonte's method revisited: An effective steepest descent method for micromagnetic energy minimization