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

Roland Pulch

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 216, issue C, 187-197

Abstract: 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.

Keywords: Ordinary differential equation; Port-Hamiltonian system; Hamiltonian function; Stochastic Galerkin method; Model order reduction; Uncertainty quantification (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:216:y:2024:i:c:p:187-197

DOI: 10.1016/j.matcom.2023.09.005

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