Keywords: dynamic domain decomposition, discrete element method, multilevel k-way graph partitioning, recursive coordinate bisection.

The paper presents a parallel three-dimensional simulation of the hopper discharge problem using the discrete element method (DEM) [1]. A soft-particle approach is adopted, in which the simulation is performed using small time increments and the contact forces between the particles are calculated using adopted contact low. The main disadvantage of the DEM is excessive computational resources. The numerical solution of industrial problems requires a large number of particles and short time steps resulting in a long computing time. Parallelization becomes an obvious option for significantly increasing the computational capabilities. During hopper discharge moving particles dynamically changes the workload configuration, making parallelization of the DEM software much more difficult and challenging. Therefore, dynamic domain decomposition is required to keep workload equally distributed between the processors.

Two alternative methods for the dynamic domain decomposition and load balancing were investigated for the case of hopper discharge flow. The first method used is the recursive coordinate bisection available in the Zoltan library. The second method employed was based on the multilevel k-way graph partitioning available in the ParMETIS library. Two alternative methods for dynamic domain decomposition were implemented in the DEMMMAT_PAR code [2] developed at the Vilnius Gediminas Technical University.

The efficiency of the considered methods and speed-up of the software developed was investigated using a series of benchmark tests simulating the granular visco-elastic frictional media in hoppers containing 0.3x10⁶ and 5x10⁶ spherical particles. The hopper discharge computations and parallel speed-up measurements were performed on the HECTOR computer (Cray XE6 system) of the EPCC in Edinburgh. Each node contained two AMD 2.3 GHz 16-core processors and 32 GB of RAM.

Quantitative comparison of the parallel performance obtained using the multilevel k-way graph partitioning and that attained by using the recursive coordinate bisection method showed benefits and drawbacks of their applicability to intensively changing workload configuration of the hopper discharge simulation. It was observed that more complex adaptation of k-way graph partitioning methods to DEM computations does not reveal higher parallel performance. Moreover, higher speed-up and lower interprocessor communication is measured employing the recursive coordinate bisection method. The speed-up equal to 1787 was measured when simulating 5 millions of particles on 2056 cores, which is comparable to the performance obtained by other researchers and reported in the literature.

1

H.P. Zhu, Z.Y. Zhou, R.Y. Yang, A.B. Yu, "Discrete particle simulation of particulate systems: A review of major applications and findings", Chemical Engineering Science, 63(23), 5728-5770, 2008.

2

R. Kacianauskas, A. Maknickas, A. Kaceniauskas, D. Markauskas, R. Balevicius, "Parallel Discrete Element Simulation of Poly-Dispersed Granular Material", Advances in Engineering Software, 41(1), 52-63, 2010.

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