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

Authors

Roland Pulch

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

Citation

• Journal: Mathematics and Computers in Simulation
• Year: 2024
• Volume: 216
• Issue:
• Pages: 187–197
• Publisher: Elsevier BV
• DOI: 10.1016/j.matcom.2023.09.005

BibTeX

@article{Pulch_2024,
  title={{Stochastic Galerkin method and port-Hamiltonian form for linear dynamical systems of second order}},
  volume={216},
  ISSN={0378-4754},
  DOI={10.1016/j.matcom.2023.09.005},
  journal={Mathematics and Computers in Simulation},
  publisher={Elsevier BV},
  author={Pulch, Roland},
  year={2024},
  pages={187--197}
}

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