An efficient parallel implementation of cell mapping methods for MDOF systems

Abstract

The long term behavior of dynamical system is usually analized by means of basins of attraction (BOA) and most often, in particular, with cell mapping methods that ensure a straightforward technique of approximation.Unfortunately the construction of BOA requires large resources, especially for higher-dimensional systems, both in term of computational time and memory space.In this paper, the implementation of cell mapping methods towards a distributed computing is undertaken; a new efficient parallel algorithm for the computation of large-scale basins of attraction is presented herein, also by addressing issues arising from the inner seriality related to the BOA construction. A cell-mapping core is thus wrapped in a management shell, in charge of the core administration, it permits to split over a multi-core environment the computing domain, by carrying out an efficient use of the distributed memory.The proposed approach makes use of a double-step algorithm in order to generate, first, the multidimensional BOA of the system and, then to evaluate arbitrary 2D Poincaré sections of the hypercube that stores the information.An analysis on a test system is performed by considering different dimensional grids; the effort of a parallel implementation towards medium and large clusters is balanced by a great results in terms of computational speed. The performances are strictly affected not only by the number of cores used to run the code, but in particular in the way they are instructed. To get the best from an implementation on a massive parallel architecture, the processes must be properly balanced between memory operations and numerical integrations.

Dynamic Cell Mapping Algorithm for Computing Basins of Attraction in Planar Filippov Systems

“…The structure of the algorithm can be easily implemented in a multi-core environment [Belardinelli & Lenci, 2016b], so that multiple analysis and subdivision processes can performed in different core processors. In the case of non planar systems the integration method used for the ESCM combined with the multidimensional cell mapping method (MDCM) [Eason & Dick, 2014;Belardinelli & Lenci, 2016a] can straightforward be integrated, to enable computation of basins of attraction in high dimensional Filippov systems. An extension of the ESCM algorithm to Filippov systems with multiple switching manifolds is directly related with the development of the integration routine as discussed in Section 3, and can be straightforwardly implemented for the case…”

“…In [Gyebrószki & Csernák, 2017] for example, the authors introduce an extension of the simple cell mapping method aimed at investigating different regions in the state space independently, to further, cluster them into a general mapping solution. Parallel processing capabilities of modern architectures have also been exploited within cell mapping methods, by considering different cell dimensions and several refinement stages [Kreuzer & Lagemann, 1996;Belardinelli & Lenci, 2016a]. However these techniques have not been extended, as far as we are aware, for discontinuous systems.…”

Robustness of attractors in tapping mode atomic force microscopy

“…Therefore, basin portraits together with integrity measures provide a means to track the basin erosion process with respect to changes in operating parameters. Hence, in order to advance the dynamical analysis of the AFM cantilever in the in-contact regime of oscillation, this section focuses on the global topology analysis by means of basins of attraction [28,29].…”

Dynamics and Stability: A Long History From Equilibrium to Dynamical Integrity

“…This represents a challenge for the future, and some initial results have yet been obtained (Fig. 36) exploiting high performance computing, such as parallel computing [59].…”