Authors

Flávio Luiz Cardoso-Ribeiro, Denis Matignon, Laurent Lefèvre

Abstract

Discretizing open systems of conservation laws while preserving the power-balance at the discrete level can be achieved using a new Partitioned Finite Element Method (PFEM), where an integration by parts is performed only on a subset of the variables in the weak formulation. Moreover, since boundary control and observation appear naturally in this formulation, the method is suitable both for simulation and control of infinite-dimensional port-Hamiltonian systems. The method can be applied using FEM software, and comes along with worked-out test cases on the 2D wave equation in different geometries and coordinate systems.

Keywords

Distributed Parameter systems; Port-Hamiltonian systems; Finite Element Method; Geometric Discretization Methods; 2D Wave equation

Citation

  • Journal: IFAC-PapersOnLine
  • Year: 2018
  • Volume: 51
  • Issue: 3
  • Pages: 119–124
  • Publisher: Elsevier BV
  • DOI: 10.1016/j.ifacol.2018.06.033
  • Note: 6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2018

BibTeX

@article{Cardoso_Ribeiro_2018,
  title={{A structure-preserving Partitioned Finite Element Method for the 2D wave equation}},
  volume={51},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2018.06.033},
  number={3},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Cardoso-Ribeiro, Flávio Luiz and Matignon, Denis and Lefèvre, Laurent},
  year={2018},
  pages={119--124}
}

Download the bib file

References