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Multigrid‐in‐time for sensitivity analysis of chaotic dynamical systems
Author(s) -
Blonigan Patrick,
Wang Qiqi
Publication year - 2017
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.1946
Subject(s) - multigrid method , sensitivity (control systems) , mathematics , chaotic , dynamical systems theory , least squares function approximation , convergence (economics) , interval (graph theory) , mathematical optimization , algorithm , computer science , mathematical analysis , partial differential equation , statistics , physics , quantum mechanics , combinatorics , electronic engineering , artificial intelligence , estimator , engineering , economics , economic growth
Summary The following paper discusses the application of a multigrid‐in‐time scheme to Least Squares Shadowing (LSS), a novel sensitivity analysis method for chaotic dynamical systems. While traditional sensitivity analysis methods break down for chaotic dynamical systems, LSS is able to compute accurate gradients. Multigrid is used because LSS requires solving a very large Karush–Kuhn–Tucker system constructed from the solution of the dynamical system over the entire time interval of interest. Several different multigrid‐in‐time schemes are examined, and a number of factors were found to heavily influence the convergence rate of multigrid‐in‐time for LSS. These include the iterative method used for the smoother, how the coarse grid system is formed and how the least squares objective function at the center of LSS is weighted.