Stokes-Dirac operator for Laplacian

Authors

Abstract

This paper proposes a particular type of Stokes-Dirac structure for describing a Laplacian used in Poisson’s equations on topologically non-trivial manifolds, i.e., not Euclidian. The operator matrix representation of the structure includes not only exterior differential operators, but also codifferential operators in the sense of the dual of the pairing between differential forms. Since the successive operation of the matrix is equivalent to the Laplace-Beltrami operator, we call it a Stokes-Dirac operator. Furthermore, the Stokes-Dirac operator is augmented by harmonic differential forms that reflect the topological geometry of manifolds. The extension enable us to describe a power balance of particular boundary energy flows on manifolds with a non-trivial shape.

Keywords

Port-Hamiltonian systems; Stokes-Dirac structures; Partial differential equations; Differential forms

Citation

Journal: IFAC-PapersOnLine
Year: 2019
Volume: 52
Issue: 16
Pages: 430–435
Publisher: Elsevier BV
DOI: 10.1016/j.ifacol.2019.11.818
Note: 11th IFAC Symposium on Nonlinear Control Systems NOLCOS 2019- Vienna, Austria, 4–6 September 2019

BibTeX

@article{Nishida_2019,
  title={{Stokes-Dirac operator for Laplacian}},
  volume={52},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2019.11.818},
  number={16},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Nishida, Gou and Maschke, Bernhard},
  year={2019},
  pages={430--435}
}

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References

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