Parallel iterative methods for variational integration applied to navigation problems

TL;DR

This paper introduces a parallel iterative approach for discrete variational methods, enhancing numerical simulations of mechanical systems and navigation problems by leveraging multicore CPUs and GPUs.

Contribution

It presents a novel parallelization strategy for discrete variational methods applied to boundary value problems, suitable for modern hardware architectures.

Findings

Effective parallelization on multicore CPUs and GPUs.

Successful application to navigation and interpolation problems.

Demonstrated excellent performance in numerical experiments.

Abstract

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.