STOCHASTIC GALERKIN METHOD AND PORT-HAMILTONIAN FORM FOR LINEAR FIRST-ORDER ORDINARY DIFFERENTIAL EQUATIONS

Authors

Roland Pulch, Olivier Sète

Abstract

We consider linear first-order systems of ordinary differential equations (ODEs) in port-Hamiltonian (pH) form. Physical parameters are remodeled as random variables to conduct an uncertainty quantification. A stochastic Galerkin projection yields a larger deterministic system of ODEs, which does not exhibit a pH form in general. We apply transformations of the original systems such that the stochastic Galerkin projection becomes structure-preserving. Furthermore, we investigate meaning and properties of the Hamiltonian function belonging to the stochastic Galerkin system. A large number of random variables implies a high-dimensional stochastic Galerkin system, which suggests itself to apply model order reduction (MOR) generating a low-dimensional system of ODEs. We discuss structure preservation in projection-based MOR, where the smaller systems of ODEs feature pH form again. Results of numerical computations are presented using two test examples.

Citation

• Journal: International Journal for Uncertainty Quantification
• Year: 2024
• Volume: 14
• Issue: 4
• Pages: 65–82
• Publisher: Begell House
• DOI: 10.1615/int.j.uncertaintyquantification.2024050099

BibTeX

@article{Pulch_2024,
  title={{STOCHASTIC GALERKIN METHOD AND PORT-HAMILTONIAN FORM FOR LINEAR FIRST-ORDER ORDINARY DIFFERENTIAL EQUATIONS}},
  volume={14},
  ISSN={2152-5080},
  DOI={10.1615/int.j.uncertaintyquantification.2024050099},
  number={4},
  journal={International Journal for Uncertainty Quantification},
  publisher={Begell House},
  author={Pulch, Roland and Sète, Olivier},
  year={2024},
  pages={65--82}
}

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