A Massively Parallel Method for Fast Computation of Invariant Manifolds

The computation of invariant manifolds in the Circular Restricted 3-Body Problem (CR3BP) is a key step in space mission design as these manifolds provide low-energy trajectories for various mission applications, including the design of gravity-assist flybys and low-energy capture and escape around bodies in the solar system. The conventional way of computing invariant manifolds involves determining the stable and unstable directions across the entire orbit through an eigendecomposition of the monodromy matrix of the periodic orbit. These directions are then propagated along the entire orbit with the state transition matrix. This paper presents a simpler method for computing invariant manifolds without relying on the monodromy matrix or its eigendecomposition, so that invariant manifolds of unstable objects besides periodic orbits can be computed. Our new algorithm is also efficiently parallelizable on modern graphics processing units, leading to speed-ups of several orders of magnitude compared to the conventional method executed on a conventional CPU.