Decision boundary maps (DBMs) are image representations of the behavior of trained machine learning classification models. They are used in examining how the model partitions its data space into decision zones separated by decision boundaries and how this partition is influenced by the training data. However, all current DBM methods require significant computational effort, which precludes their use in interactive visual analytics scenarios. We present FastDBM, a set of techniques for the fast computation of DBMs. Our methods can accelerate any existing DBM algorithm by over one order of magnitude, yield results very similar to the original DBM methods, have a single parameter to set (with good presets), and are simple to implement. We demonstrate our method on various combinations of DBM techniques, datasets, and classification models.