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

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  • Pulch, Roland

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.

Suggested Citation

  • Pulch, Roland, 2024. "Stochastic Galerkin method and port-Hamiltonian form for linear dynamical systems of second order," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 216(C), pages 187-197.
    • Handle: RePEc:eee:matcom:v:216:y:2024:i:c:p:187-197
    DOI: 10.1016/j.matcom.2023.09.005
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    1. Pulch, Roland, 2018. "Model order reduction and low-dimensional representations for random linear dynamical systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 144(C), pages 1-20.
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