A parallel implementation of a fast algorithm for solving systems of the Smoluchowski-type kinetic equations of aggregation and fragmentation processes is proposed. The efficiency and scalability of the proposed implementation are shown for several particular problems of aggregation and fragmentation kinetics. The oscillatory solutions of the Cauchy problems are found using the developed parallel algorithm in terms of total density.

Keywords: Smoluchowski equation, kinetics of aggregation and fragmentation processes, predictor-corrector scheme, cross interpolation method, low-rank matrix approximations, discrete convolution, parallel computing.

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