Hybrid deterministic/stochastic algorithm for large sets of rate equations

We propose a hybrid algorithm for the time integration of large sets of rate equations coupled by a relatively small number of degrees of freedom. A subset containing fast degrees of freedom evolves deterministically, while the rest of the variables evolves stochastically. The emphasis is put on the coupling between the two subsets, in order to achieve both accuracy and efficiency. The algorithm is tested on the problem of nucleation, growth and coarsening of clusters of defects in iron, treated by the formalism of cluster dynamics. We show that it is possible to obtain results indistinguishable from fully deterministic and fully stochastic calculations, while speeding up significantly the computations with respect to these two cases.