A first parallel programming approach in basins of attraction computation

• Application of parallel programming to the basins of attraction computation.
• Inner seriality arising in the basins of attraction computation analyzed and tackled.
• Two parallel codes developed and tested.
• Optimal time balance and working load on computing nodes.

The paper focuses on the development of a numerical code for the computation of basins of attraction by using the parallel programming. Two different approaches based on the massage passing interface (MPI) standard are presented; the performance analysis presented encourages us to use a massive communication between nodes only for a few-cores architecture. The critical issues arising from the study of a generic dynamical system are discussed while the computation of basins is performed on a benchmark system described by Duffing׳s equation. We paid attention at the optimization of the computing time as well as the work time load on each node in order to develop a performing and portable code. For the presented codes, both the scalability with an implementation on a professional cluster and the capabilities of the parallelism in the elaborations of basins with a large set of initial conditions have been tested.