Authors

Babak Maboudi Afkham, Jan S. Hesthaven

Abstract

Reduced basis methods are popular for approximately solving large and complex systems of differential equations. However, conventional reduced basis methods do not generally preserve conservation laws and symmetries of the full order model. Here, we present an approach for reduced model construction, that preserves the symplectic symmetry of dissipative Hamiltonian systems. The method constructs a closed reduced Hamiltonian system by coupling the full model with a canonical heat bath. This allows the reduced system to be integrated with a symplectic integrator, resulting in a correct dissipation of energy, preservation of the total energy and, ultimately, it helps conserving the stability of the solution. Accuracy and stability of the method are illustrated through the numerical simulation of the dissipative wave equation and a port-Hamiltonian model of an electric circuit.

Keywords

Model order reduction; Symplectic model reduction; The reduced dissipative Hamiltonian method

Citation

  • Journal: Journal of Scientific Computing
  • Year: 2019
  • Volume: 81
  • Issue: 1
  • Pages: 3–21
  • Publisher: Springer Science and Business Media LLC
  • DOI: 10.1007/s10915-018-0653-6

BibTeX

@article{Maboudi_Afkham_2018,
  title={{Structure-Preserving Model-Reduction of Dissipative Hamiltonian Systems}},
  volume={81},
  ISSN={1573-7691},
  DOI={10.1007/s10915-018-0653-6},
  number={1},
  journal={Journal of Scientific Computing},
  publisher={Springer Science and Business Media LLC},
  author={Maboudi Afkham, Babak and Hesthaven, Jan S.},
  year={2018},
  pages={3--21}
}

Download the bib file

References

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