Keywords: domain decomposition, implicit integration, granular matter, discrete element method, backward acting grate, parallel computing.

An implicit discretization is used to calculate the state of the particles. The state of particles at the next time step is calculated not only from the current and previous time steps but also from the next time step so that the equations of motion will be implicit with respect to new positions. Generally, each time step in the implicit method demands more computations than a single time step in explicit schemes because a system of equations needs to be solved in implicit methods. On the other hand, relatively larger time steps could be used in implicit methods due to the higher numerical stability.

An efficient parallel algorithm is implemented based on domain decomposition technique called orthogonal recursive bisection (ORB) [3]. The algorithm uses a linked-cell structure to divide the domain into cells and store the particles in the cells based on their position. The cell approach significantly reduces the time for neighbourng particle search since the search is limited to the particles in own cells and their immediate neighbouring cells. The message passing interface (MPI) libraries are used as message exchange porotcol. In order to increase the efficiency of the parallel computation non-blocking communication is used.

Qualitative comparison of the numerical and experimental results indicates the capability of the proposed methodology to analyse the residence time behaviour of solid particles on a backward acting grate. The measured parallel performance [4] shows the implemented parallel algorithm achieved an efficiency of more than 80% using eight processors.

1

J. Duran, P.G. De Gennes, "Sands, powders, and grains: An introduction to the physics of granular material", Springer, 90(4), 32-43, 1999. doi:10.1063/1.1383168

2

P. Richard, "Slow relaxation and compaction of granular systems", Nature Materials, 4, 121-128, 2005. doi:10.1038/nmat1300

3

M.J. Berger, S.H. Bokhari, "A partitioning strategy for nonuniform problems on multiprocessors", IEEE Transactions on Computers, 36(5), 570-580, 1987. doi:10.1109/TC.1987.1676942

4

A.H. Karp, H.P. Flatt, "Measuring Parallel Processor Performance", Communications of the ACM, 33(5), 539-543, 1990. doi:10.1145/78607.78614

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