Least Squares Shadowing sensitivity analysis of chaotic limit cycle oscillations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:267

Article

Wang, Qiqi¹  Hu, Rui¹  Blonigan, Patrick¹ 

[1] MIT, Cambridge, MA 02139 USA

关键词: Sensitivity analysis;    Linear response;    Adjoint equation;    Unsteady adjoint;    Chaos;    Statistics;    Climate;    Least squares shadowing;   

DOI  :  10.1016/j.jcp.2014.03.002

来源: Elsevier

【 摘 要 】

The adjoint method, among other sensitivity analysis methods, can fail in chaotic dynamical systems. The result from these methods can be too large, often by orders of magnitude, when the result is the derivative of a long time averaged quantity. This failure is known to be caused by ill-conditioned initial value problems. This paper overcomes this failure by replacing the initial value problem with the well-conditioned least squares shadowing (LSS) problem. The LSS problem is then linearized in our sensitivity analysis algorithm, which computes a derivative that converges to the derivative of the infinitely long time average. We demonstrate our algorithm in several dynamical systems exhibiting both periodic and chaotic oscillations. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free