Cluster dynamics in materials: a hybrid deterministic/stochastic coupling algorithm

Pierre Terrier
École Nationale des Ponts-et-Chaussées

Cluster dynamics method is an efficient method to study the aging of materials under irradiation. It consists in solving a set of rate equations describing the evolution of the concentration of clusters of various sizes. However, it becomes computationally prohibitive when large clusters appear. In order to reduce the numerical complexity of the model, we develop a versatile coupling between rate equations and two stochastic approaches. The first one is a jump process that exactly describes the dynamics. The second one is based on a limiting model, in the form of a Fokker-Planck equation. We propose a stochastic approach to solve this equation. The coupling method allows to simultaneously evolve the rate equations (for small size clusters) and the stochastic part. The accuracy of this hybrid deterministic/stochastic coupling algorithm is studied on a simple case. We also report results for complex materials with different types of defects.

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