Stochastic Galerkin method and port-Hamiltonian form for linear dynamical systems of second order

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.

Automated summary

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.