Imperial College London
Alternate

ProfessorGeorgePapadakis

Faculty of Engineering, Department of Aeronautics

Professor of Aerodynamics
 
 
 
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Contact

 

+44 (0)20 7594 5080g.papadakis

 
 
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Location

 

331City and Guilds BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Shawki:2019:10.1016/j.jcp.2019.108861,
author = {Shawki, K and Papadakis, G},
doi = {10.1016/j.jcp.2019.108861},
journal = {Journal of Computational Physics},
pages = {1--19},
title = {A preconditioned Multiple Shooting Shadowing algorithm for the sensitivity analysis of chaotic systems},
url = {http://dx.doi.org/10.1016/j.jcp.2019.108861},
volume = {398},
year = {2019}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - We propose a preconditioner that can accelerate the rate of convergence of the Multiple Shooting Shadowing (MSS) method [1]. This recently proposed method can be used to compute derivatives of time-averaged objectives (also known as sensitivities) to system parameter(s) for chaotic systems. We propose a block diagonal preconditioner, which is based on a partial singular value decomposition of the MSS constraint matrix. The preconditioner can be computed using matrix-vector products only (i.e. it is matrix-free) and is fully parallelised in the time domain. Two chaotic systems are considered, the Lorenz system and the 1D Kuramoto Sivashinsky equation. Combination of the preconditioner with a regularisation method leads to tight bracketing of the eigenvalues to a narrow range. This combination results in a significant reduction in the number of iterations, and renders the convergence rate almost independent of the number of degrees of freedom of the system, and the length of the trajectory that is used to compute the time-averaged objective. This can potentially allow the method to be used for large chaotic systems (such as turbulent flows) and optimal control applications. The singular value decomposition of the constraint matrix can also be used to quantify the effect of the system condition on the accuracy of the sensitivities. In fact, neglecting the singular modes affected by noise, we recover the correct values of sensitivity that match closely with those obtained with finite differences for the Kuramoto Sivashinsky equation in the light turbulent regime. We notice a similar improvement for the Lorenz system as well.
AU  - Shawki,K
AU  - Papadakis,G
DO  - 10.1016/j.jcp.2019.108861
EP  - 19
PY  - 2019///
SN  - 0021-9991
SP  - 1
TI  - A preconditioned Multiple Shooting Shadowing algorithm for the sensitivity analysis of chaotic systems
T2  - Journal of Computational Physics
UR  - http://dx.doi.org/10.1016/j.jcp.2019.108861
UR  - https://www.sciencedirect.com/science/article/pii/S0021999119305455?via%3Dihub
UR  - http://hdl.handle.net/10044/1/72202
VL  - 398
ER  -
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