期刊
MATHEMATICS AND COMPUTERS IN SIMULATION
卷 216, 期 -, 页码 187-197出版社
ELSEVIER
DOI: 10.1016/j.matcom.2023.09.005
关键词
Ordinary differential equation; Port-Hamiltonian system; Hamiltonian function; Stochastic Galerkin method; Model order reduction; Uncertainty quantification
This paper investigates second-order linear dynamical systems and applies uncertainty quantification. Through the stochastic Galerkin method and structure-preserving model order reduction, high-dimensional and small second-order linear dynamical systems are obtained. Additionally, a Hamiltonian function describing internal energy is proposed, and its properties for the stochastic Galerkin systems are examined.
We investigate linear dynamical systems of second order. Uncertainty quantification is applied, where physical parameters are substituted by random variables. A stochastic Galerkin method yields a linear dynamical system of second order with high dimensionality. A structure-preserving model order reduction (MOR) produces a small linear dynamical system of second order again. We arrange an associated port-Hamiltonian (pH) formulation of first order for the second-order systems. Each pH system implies a Hamiltonian function describing an internal energy. We examine the properties of the Hamiltonian function for the stochastic Galerkin systems. We show numerical results using a test example, where both the stochastic Galerkin method and structure-preserving MOR are applied.(c) 2023 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
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