DocumentCode :
3362944
Title :
A localized symplectic model reduction technique for parameterized Hamiltonian systems
Author :
Liqian Peng ; Mohseni, Kamran
Author_Institution :
Dept. of Mech. & Aerosp. Eng., Univ. of Florida, Gainesville, FL, USA
fYear :
2015
fDate :
1-3 July 2015
Firstpage :
5545
Lastpage :
5550
Abstract :
In this article, a localized symplectic model reduction technique, locally weighted proper symplectic decomposition (LWPSD), is proposed to simplify parameterized Hamiltonian systems. Our aim is two-fold. First, to achieve computational savings for large-scale Hamiltonian systems with parameter variation. Second, to preserve the symplectic structure of the original system. As an analogy to the proper orthogonal decomposition, the proper symplectic decomposition (PSD) can be used to construct a symplectic subspace to fit empirical data, and yield a low-order Hamiltonian system on the subspace. Instead of using a global basis to construct a global reduced model, the locally weighted approach approximates the original system by multiple lower-dimensional subspaces. Each local reduced basis is generated by the PSD of a weighted snapshot ensemble. Compared with the standard PSD, the LWPSD could yield a more accurate solution with a fixed subspace dimension. The stability, accuracy, and efficiency of the proposed technique are illustrated through the numerical simulation of the wave equation.
Keywords :
large-scale systems; reduced order systems; stability; wave equations; LWPSD; global reduced model; large-scale Hamiltonian systems; localized symplectic model reduction technique; locally weighted proper symplectic decomposition; low-order Hamiltonian system; parameterized Hamiltonian systems; proper orthogonal decomposition; stability; wave equation; weighted snapshot ensemble; Computational modeling; Mathematical model; Method of moments; Propagation; Reduced order systems; Time-domain analysis; Trajectory;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
American Control Conference (ACC), 2015
Conference_Location :
Chicago, IL
Print_ISBN :
978-1-4799-8685-9
Type :
conf
DOI :
10.1109/ACC.2015.7172207
Filename :
7172207
Link To Document :
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