Efficient parallel inversion of ParaOpt preconditioners
Numerical Analysis
2024-12-04 v1 Numerical Analysis
Optimization and Control
Abstract
Recently, the ParaOpt algorithm was proposed as an extension of the time-parallel Parareal method to optimal control. ParaOpt uses quasi-Newton steps that each require solving a system of matching conditions iteratively. The state-of-the-art parallel preconditioner for linear problems leads to a set of independent smaller systems that are currently hard to solve. We generalize the preconditioner to the nonlinear case and propose a new, fast inversion method for these smaller systems, avoiding disadvantages of the current options with adjusted boundary conditions in the subproblems.
Cite
@article{arxiv.2412.02425,
title = {Efficient parallel inversion of ParaOpt preconditioners},
author = {Corentin Bonte and Arne Bouillon and Giovanni Samaey and Karl Meerbergen},
journal= {arXiv preprint arXiv:2412.02425},
year = {2024}
}