并行加速的局部变分迭代法及其轨道计算应用

为满足航天工程对轨道计算精度和实时性的高要求,近年来发展出了可以通过大步长积分修正实现快速精确求解的积分修正类方法.积分修正类方法有可并行计算的特点,然而在串行计算环境下会受到计算资源的限制,无法充分发挥其可并行加速的优势.此外,合理的计算参数通常难以预先确定,也使积分修正类方法大步长快速计算的优势难以充分体现.针对以上问题,利用积分修正类方法可并行计算的特点,提出了并行加速的局部变分迭代法PA-LVIM,通过将传统局部变分迭代法LVIM的并行计算量均摊到多个计算节点上,显著提高了计算速度.此外,还使用根据系统状态二阶导数分布确定计算参数的打磨法优化了PA-LVIM的计算参数,进一步发挥了其大步长快速计算的优势.求解了三个经典的轨道递推问题,仿真结果表明, PA-LVIM的加速效果明显,且经打磨法优化计算参数后,其计算效率又进一步得到提高,将当前主流方法的计算效率提高了5倍以上.

PARALLEL ACCELERATED LOCAL VARIATIONAL ITERATION METHOD AND ITS APPLICATION IN ORBIT COMPUTATION

In recent years, a family of methods based on integral correction have been developed to address the increasing requirements of accuracy and efficiency of orbit computation in aerospace engineering. These methods are fast and accurate via integral correction in a large domain, but limited by scarceness of computing resources in serial computing environment. The serial computing is essentially a waste of the advantage of the integral correction type methods which can support parallel computing. In addition, the appropriate calculation parameters of these methods are usually difficult to determine. That makes it difficult to to choose a proper large step size to ensure both accuracy and efficiency. For the above issues, a parallel accelerated local variation iteration method (PA-LVIM) is presented in this paper based on the local variation iteration method (LVIM) which is a classical method based on integral correction. By exploiting parallel computing, the amount of computational burden in the LVIM is distributed to multiple computing nodes so as to accelerate the computing speed. In addition, the calculation parameters of the PA-LVIM are optimized by a novel polishing mesh refinement method, which divides the integration stepsize according to the second derivatives of the dynamic system states. Three classical orbit propagation problems are solved to verify the validity of the proposed PA-LVIM. Simulation results show that the PA-LVIM is dramatically accelerated, and its computational efficiency is further improved in combination with the polishing mesh refinement method, which increases the efficiency of current methods by more than 5 times.