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Sensitivity analysis on chaotic dynamical systems by Non-Intrusive Least Squares Shadowing (NILSS)

Author(s)
Ni, Angxiu
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Massachusetts Institute of Technology. Department of Aeronautics and Astronautics.
Advisor
Qiqi Wang.
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MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission. http://dspace.mit.edu/handle/1721.1/7582
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Abstract
This thesis develops the Non-Intrusive Least Squares Shadowing (NILSS) method, which computes the sensitivity for long-time averaged objectives in chaotic dynamical systems. In NILSS, we represent a tangent solution by a linear combination of one inhomogeneous tangent solution and several homogeneous tangent solutions. Next, we solve a least squares problem using this representation; thus, the resulting solution can be used for computing sensitivities. NILSS is easy to implement with existing solvers. In addition, for chaotic systems with many degrees of freedom but few unstable modes, NILSS has a low computational cost. NILSS is applied to two chaotic PDE systems: the Lorenz 63 system and a CFD simulation of flow over a backward-facing step. In both cases, the sensitivities computed by NILSS reflect the trends in the long-time averaged objectives of dynamical systems.
Description
Thesis: S.M., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2017.
 
Cataloged from PDF version of thesis.
 
Includes bibliographical references (pages 61-63).
 
Date issued
2017
URI
http://hdl.handle.net/1721.1/112475
Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Publisher
Massachusetts Institute of Technology
Keywords
Aeronautics and Astronautics.

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