Resumo:
GPU PARALLELIZATION OF N-BODY ALGORITHMS AND APPLICATIONS TO EXTRASOLAR PLANETARY SYSTEMS Alan Costa de Souza ABSTRACT In this thesis, we analyzed the feasibility and implemented the parallelization of algorithms to solve the planetary equations of motion on GPU cards. Based on the sequential version of the Helio algorithm, which is part of the Swifter software, we made the translation of the code from Fortran to C and then its parallelization in CUDA. We tested three different approaches to parallelization: (i) the symplectic algorithm of Ruth for a system of N bodies, with N large, (ii) the Helio algorithm also for a system of many bodies, and (iii) the Helio algorithm applied to a grid of initial conditions for a few-body problem. We conclude that the parallelized versions of both the Ruth algorithm and the grid of initial conditions are much more computationally efficient than their serial counterparts. On the other hand, the Helio algorithm applied to a many body system shows a performance with respect to the serial version that depends on the GPU cards and CPUs used. Together with the parallelization, we implemented the calculation of some chaos indicators, in particular the MEGNO indicator, and we validate our code by reproducing well known results from the literature. Finally, we applied the code that parallelizes a grid of initial conditions to the study of the stability of three extra-solar planetary systems: Kepler-419, Kepler-59 and Kepler-46. The interest on these systems is because their dynamical parameters have been obtained through the analysis of transit timing variations, and we want to verify whether the systems are stable or not within the uncertainties of their parameters. KEYWORDS N-body problem; extrasolar planets; chaos; GPU acceleration
