This thesis is dedicated to computational micromagnetics, where several new numerical methods are developed. All concepts rely, at some point, on representation of the macroscopic magnetization on tensor grids. In this context, the data-sparse representation or approximation via tensor formats serves as a key motivation. Much attention is paid to the computation of the stray field. A novel method determines the demagnetizing field on a tensor grid with help of data-sparse tensor format representation of magnetization components. Kronecker product structure of the demagnetizing field operator is shown. Also, the Hessian of the discretized total magnetic Gibbs free energy permits a Kronecker product form. This allows cheap and efficient evaluation of the energy and computation of the gradient for tensor structured input. Furthermore, the described method is even accelerated with help of fast Fourier transform. A detailed overview of micromagnetic energy minimization is given, including a new method that is a variation of steepest descent. On this basis, energy minimization with structured tensor magnetization is considered. A sublinearly scaling low-rank algorithm is introduced, which relies on successive rank-k updates. The approach addresses the computation of equilibrium states and hysteresis of large ferromagnetic particles on rectangular grids. In order to address micromagnetic simulations on unstructured finite element meshes, a further novel demagnetizing field method, based on non-uniform fast Fourier transform, is developed.