The Parallel Simulation Method for d-dimensional Abelian Sandpile Automata
Keywords:
Abelian sandpile model, Dense packing problem, Parallel algorithm, Cellular automataAbstract
In this paper, the star-packing problem introduced in [1] for a square lattice is generalized for d-dimensional lattice Ld, d ∈ N. The problem is to pack the lattice Ld with star graphs S2d. Using the solution of this problem, a parallel algorithm for the simulation of d-dimensional cellular automata is developed. As an example of cellular automata, the relaxation process of unstable states of Abelian sandpile model is considered. Appropriate software packages have been developed using OpenMP and CUDA technologies. The parallel simulation results, carried out for 3-dimensional lattices of different sizes, are presented.
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