论文标题
一种平行的迭代方法，用于变分集成
A parallel iterative method for variational integration
论文作者
论文摘要
离散的变分方法在不同机械系统的数值模拟中表现出卓越的性能。在本文中，我们介绍了一个迭代程序，以解决边界价值问题的离散变分方程。更具体地说，我们探索了一种并行化策略，该策略利用了多核CPU和GPU（图形卡）的功能。我们研究了这种高阶拉格朗日系统的平行方法，该方法出现在全面的问题及其他地区。本文最重要的部分是针对这些方法的不同收敛条件进行的精确研究。我们在一些有趣的例子中说明了它们的出色行为，即Zermelo的导航问题，燃料最佳的导航问题，插值问题或在天体动力学中受控4体问题的燃油优化问题，表明我们方法的潜力。
Discrete variational methods show excellent performance in numerical simulations of different mechanical systems. In this paper, we introduce an iterative procedure for the solution of discrete variational equations for boundary value problems. More concretely, we explore a parallelization strategy that leverages the capabilities of multicore CPUs and GPUs (graphics cards). We study this parallel method for higher-order Lagrangian systems, which appear in fully-actuated problems and beyond. The most important part of the paper is devoted to a precise study of different convergence conditions for these methods. We illustrate their excellent behavior in some interesting examples, namely Zermelo's navigation problem, a fuel-optimal navigation problem, interpolation problems or in a fuel optimization problem for a controlled 4-body problem in astrodynamics showing the potential of our method.
