Parallel time methods for computing a satellite's trajectory -

Abstract

Solving time dependent ordinary differential equations in a time-parallel way was thought to be impossible since time integration is inherently sequential. However in recent years, several predictor-corrector schemes have been proposed in order to solve time dependent differential equations. The most prominent of these algorithms is the well known Parareal algorithm (Lions et al 2001,Gander et al 2007) and more recently the Adaptive Parallel Time Integration algorithm ``APTI''(Nassif et al 2005). Such method has been successfully applied to the problem that models the motion of a membrane element linked to a spring (Karam, Nassif, Erhel 2013). In this thesis, we implement APTI in order to calculate the trajectory of a satellite, governed by a perturbed Keplerian model. We present also a modified version of the Parareal algorithm that utilizes the convergence of some slices prior to the global convergence, in order to enhance execution time. In order to test the efficiency of APTI, we compare its results with those obtained by Parareal and Modified Parareal. We show speed-ups as well as deviation from trajectories computed on the basis of a sequential algorithm, indicating the efficiency of the APTI approach for relatively large periods of time.