We propose a method for the stray-field computation of ferromagnetic microstructures via the magnetic scalar potential. The scalar potential is computed using the convolution theorem and the fast Fourier transform. For the discrete convolution an analytical expression for the scalar potential of a uniformly magnetized cuboid is presented. A performance gain of up to 55\% compared to common simulation codes is achieved and the memory consumption is reduced by 30\%. Since the stray-field computation is the most time consuming part of micromagnetic simulations, this performance gain strongly influences the overall performance. The low memory consumption allows simulations with a high number of simulation cells. This enables simulations of large systems like arrays of coupled magnetic vortices or simulations with high spatial resolution. In conjunction with modern hardware, simulations of microstructures with atomic resolution become feasible.