Discrete variational methods have shown an excellent performance in numerical simulations of different mechanical systems. In this paper, we introduce an iterative method for discrete variational methods appropriate for boundary value problems. More concretely, we explore a parallelization strategy that leverages the power of multicore CPUs and GPUs (graphics cards). We study this parallel method for first-order and second-order Lagrangians and we illustrate its excellent behavior in some interesting applications, namely Zermelo's navigation problem, a fuel-optimal navigation problem, and an interpolation problem.

中文翻译：

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应用于导航问题的变分积分的并行迭代方法

离散变分方法在不同机械系统的数值模拟中表现出优异的性能。在本文中，我们介绍了一种适用于边界值问题的离散变分方法的迭代方法。更具体地说，我们探索了一种利用多核 CPU 和 GPU（图形卡）功能的并行化策略。我们研究了这种用于一阶和二阶拉格朗日函数的并行方法，并在一些有趣的应用中说明了它的出色表现，即 Zermelo 导航问题、燃料优化导航问题和插值问题。