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Computer simulations of the microscopic magnetic dynamics of thin films provides a means for developing theoretical understanding of the behavior of magnetic recording materials and a way of relating material parameters to magnetic behavior. Such simulations have become possible because of the availability of high-performance supercomputers (such as the Connection Machine) and by improvements in algorithms for evaluating magnetic interactions. The proper implementation of the Fourier technique on a two-dimensional hexagonal lattice is described. A naive transcription of the method as used for a rectangular lattice leads to serious aliasing problems for short wavelengths. The implementation described reduces these effects.