We present an improved micromagnetic model for predicting the minimum energy magnetization states in fine magnetite grains. The resolution, or the number of elemental magnetization vectors, has been increased over previous models: first, by the use of a Fourier transform algorithm to reduce the number of calculations from (N2) to (N log N) (N being the number of elements into which the grain is subdivided); and second, by implementing the model on a parallel computer. Using a parallel computer reduces the computation time by a factor of approximately 1/(4Np), where Np represents the number of processors. The improved model enables equilibrium magnetization states to be predicted using a resolution of 64¿64¿64 subcubes to a grain in 16 hours of CPU time; this compares with a resolution of 12¿12¿12 in 24 hours of CPU time for previous models. High-resolution models allow the examination of multidomain states in materials such as magnetite and different sized grains or assemblages of interacting grains.¿ 1997 American Geophysical Union