A Partitioned Finite Element Method for the Structure-Preserving Discretization of Damped Infinite-Dimensional Port-Hamiltonian Systems with Boundary Control

Authors

Anass Serhani, Denis Matignon, Ghislain Haine

Abstract

Many boundary controlled and observed Partial Differential Equations can be represented as port-Hamiltonian systems with dissipation, involving a Stokes-Dirac geometrical structure together with constitutive relations. The Partitioned Finite Element Method, introduced in Cardoso-Ribeiro et al. (2018), is a structure preserving numerical method which defines an underlying Dirac structure, and constitutive relations in weak form, leading to finite-dimensional port-Hamiltonian Differential Algebraic systems (pHDAE). Different types of dissipation are examined: internal damping, boundary damping and also diffusion models.

Keywords

Port-Hamiltonian systems; Dissipation; Structure preserving method; Partitioned Finite Element Method

Citation

• ISBN: 9783030269791
• Publisher: Springer International Publishing
• DOI: 10.1007/978-3-030-26980-7_57
• Note: International Conference on Geometric Science of Information

BibTeX

@inbook{Serhani_2019,
  title={{A Partitioned Finite Element Method for the Structure-Preserving Discretization of Damped Infinite-Dimensional Port-Hamiltonian Systems with Boundary Control}},
  ISBN={9783030269807},
  ISSN={1611-3349},
  DOI={10.1007/978-3-030-26980-7_57},
  booktitle={{Geometric Science of Information}},
  publisher={Springer International Publishing},
  author={Serhani, Anass and Matignon, Denis and Haine, Ghislain},
  year={2019},
  pages={549--558}
}

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References

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