A PARALLEL ITERATIVE METHOD FOR VARIATIONAL INTEGRATION
Ferraro SJ, Martín de Diego D, Sato Martín de Almagro RT (2025)
Publication Type: Journal article
Publication year: 2025
Journal
Book Volume: 12
Pages Range: 528-553
Journal Issue: 4
DOI: 10.3934/jcd.2025006
Abstract
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. It consists in repeatedly correcting the position of the non-boundary points of a proposed discrete path in order to converge to a solution. This is accomplished using a parallelization strategy that leverages the capabilities of multicore CPUs and GPUs. Further, we develop this parallel method for higher-order Lagrangian systems, which appear in fully-actuated problems and beyond. Convergence conditions for this kind of method are investigated. 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.
Involved external institutions
Universidad Nacional del Sur
Argentina (AR)
Instituto de Ciencias Matemáticas (ICMAT) / Institute of Mathematical Sciences
Spain (ES)
Argentina (AR)
Instituto de Ciencias Matemáticas (ICMAT) / Institute of Mathematical Sciences
Spain (ES)
How to cite
APA:
Ferraro, S.J., Martín de Diego, D., & Sato Martín de Almagro, R.T. (2025). A PARALLEL ITERATIVE METHOD FOR VARIATIONAL INTEGRATION. Journal of Computational Dynamics, 12(4), 528-553. https://doi.org/10.3934/jcd.2025006
MLA:
Ferraro, Sebastián J., David Martín de Diego, and Rodrigo Takuro Sato Martín de Almagro. "A PARALLEL ITERATIVE METHOD FOR VARIATIONAL INTEGRATION." Journal of Computational Dynamics 12.4 (2025): 528-553.
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