Marchenko M.A.  

Study of efficiency of parallel stochastic simulation algorithm to solve coagulation equation

For numerical analysis of spatially inhomogeneous coagulation process, we present new parallel Direct Simulation Monte Carlo algorithm. The algorithm is based on simulation of multiparticle ensembles using domain decomposition and splitting techniques. To study accuracy and efficiency of the parallel algorithm, we consider the spatially inhomogeneous coagulation equation with known analytical solution. Namely, to investigate deterministic and statistical errors of the algorithm with respect to its parameters (initial number of test particles, time step size, regularization parameter of the coagulation kernel), we perform high precision computations on high-performance computer using the software library PARMONC which was developed by the author earlier. We also study the efficiency and speed-up of the parallel algorithm in the scenario when we increase both the number of processors and initial number of particles (and also changing other parameters of the algorithm) to enable better accuracy of simulation.

This work was partially supported by the grants of the Russian Foundation for Basic Research No. 15-01-00894, 15-01-08988, 13-01-00746, 15-01-09230 and 13-07-00589; Program of Fundamental Research of the Presidium of the Russian Academy of Sciences No. 43.

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