Multigrid-in-time for sensitivity analysis of chaotic dynamical systems
Author(s)Blonigan, Patrick Joseph; Wang, Qiqi
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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.
DepartmentMassachusetts Institute of Technology. Department of Aeronautics and Astronautics
Numerical Linear Algebra with Applications
Blonigan, Patrick, and Qiqi Wang. “Multigrid-in-Time for Sensitivity Analysis of Chaotic Dynamical Systems: MULTIGRID-IN-TIME FOR CHAOTIC SENSITIVITY ANALYSIS.” Numerical Linear Algebra with Applications (2014): n. pag.