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A Fast Stratified Sampling Simulation of Coagulation Processes

We develop a new version of the direct simulation Monte Carlo method for coagulation processes governed by homogeneous Smoluchowsky equations. The method is based on a subdivision of the set of particle pairs into classes, and on an efficient algorithm for sampling from a discrete distribution, the so-called Walker's alias method. The efficiency of the new method is drastically increased compared to the conventional methods, especially when the coagulation kernel is strongly varying. The method is applied to solving a problem of islands formation on a surface due to a diffusion controlled coagulation