A heterogeneous computing algorithm for two-dimensional unstable manifolds of time-continuous systems

Abstract

Two-dimensional manifolds usually contain many nonlinear behaviors in complicate structures, which implies that much numerical calculation must be done during computing. Therefore, how to accomplish the work efficiently is a key problem. Since today’s computers tend to heterogeneous platforms including multi-core CPUs and general purpose GPUs, this paper proposes a fast manifold computing algorithm, which is not only of high precision and versatility, but also very suited to the new generation of computers. The algorithm contains two kinds of computation: extending trajectories and generating triangles. The former is large and simple, which is suitable for GPU; the later is small and complicate, which is suitable for CPU. The computation for the stable manifold of the Lorenz system at the origin shows that this algorithm ensures the best performance of heterogeneous platforms and improve the computing speed greatly.