中文摘要：

非线性系统的二维流形通常具有复杂几何结构和丰富动力学信息,因此在流形计算与可视化时存在大量的不可避免的数值计算.因此,如何高效地完成这些计算就成了关键问题.鉴于当今计算机的异构发展趋势（包含多核CPU和通用GPU）,本文在兼顾精度和通用性的基础上,提出了适用于新一代计算平台的快速流形计算方法.本算法将计算任务分为轨道延伸和三角形生成两部分,前者运算量大而单一适合GPU完成,后者运算量小而复杂适合CPU执行.通过对Lorenz系统原点稳定流形的计算,表明本算法能充分发挥异构平台的综合性能,可大幅度提高计算速度.

英文摘要：

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.