Multigrid‐in‐time for sensitivity analysis of chaotic dynamical systems
Abstract
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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jul 02, 2014
- Source ID
- 10.1002/nla.1946
Entities
People
- Patrick Blonigan
- Qiqi Wang
Organizations
- Massachusetts Institute of Technology
- United States Department of Defense