Micromagnetics is a classical model of magnetism in magnetic materials, operative at the nanometer length scale. Typical micromagnetic simulations model magnetic parts of dimensions ranging from tens of nanometers up to a few micrometers. The most computationally expensive portion of a micromagnetic simulation is the evaluation of the long-range self-magnetostatic (aka dipole or demagnetizing) field. In this talk I will provide some history of micromagnetics at NIST, and discuss in detail some of the numerical and computational challenges involved in a fast, accurate method for computing the demagnetizing field in a simulation with periodic boundaries. Michael Donahue is a mathematician in the Applied and Computational Mathematics Division at the National Institute of Standards and Technology (NIST) in Gaithersburg, Maryland, where he does research on micromagnetics and leads development of the OOMMF public domain micromagnetics package. Prior to joining NIST, he was an industrial postdoctoral research associate at the IMA, working in conjunction with Siemens Corporate Research on artificial neural networks and computer vision. Dr. Donahue holds PhDs in mathematics and engineering from The Ohio State University, and has authored over 50 journal publications.