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We present a fast computer simulation algorithm for high dimensional barrier crossing simulations. The algorithm is described with reference to the Graham and Olmsted (GO) model of flow-induced nucleation in polymers [R. S. Graham and P. D. Olmsted, Phys. Rev Lett. 103, 115702 (2009)]. Inspired by Chandler's barrier crossing algorithm [D. Chandler, J. Chem. Phys 68, 2959 (1978)], our algorithm simulates only the region around the top of the nucleation barrier, where the system deviates most strongly from equilibrium. When applied to the kinetic Monte Carlo (kMC) routine used in the GO model, our algorithm has two advantages: it requires very little additional coding; and it is simple enough to be applied to any barrier crossing problem that can be written in terms of a kMC simulation. Our fast nucleation algorithm is shown to vastly decrease the computer time required to perform the kMC simulations of high barrier crossing.

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