Journal of Theoretical
and Applied Mechanics
0, 0, pp. , Warsaw 0

Multi-core and many-core SPMD parallel algorithms for construction of basins of attractions

Marcos Silveira, Paulo J P Gonçalves, José M Balthazar
Construction of basins of attraction, used for the analysis of nonlinear dynamical systems which present multistability are computationaly very expensive. Because of the long runtime needed, in many cases the construction of the basins does not have any practical use. Numerical time integration is currently the bottleneck of algorithms used for construction of such basins. The integrations related to each set of initial conditions are independent of each other. The assignment of each integration to a separate thread seems very attractive, and parallel algorithms which use this approach to construct the basins are presented here. Two versions are considered, one for multi-core and another for many-core arquitectures, both based on a SPMD approach. The algorithm is tested on two systems, the classic nonlinear Duffing system, a non-ideal system presenting the Sommerfeld Effect and an immunodynamic system. The results for all examples demonstrate the versatility of the proposed parallel algorithm, showing that the multi--core parallel algorithm using MPI has nearly ideal speedup and efficiency.
Keywords: basins of attraction; MPI; CUDA; Duffing equation; Sommerfeld effect; immunodynamics

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