Structure Preserving Finite Differences in Polar Coordinates for Heat and Wave Equations.

Authors

Vincent Trenchant, Weiwei Hu, Hector Ramirez, Yann Le Gorrec

Abstract

This paper proposes a finite difference spatial discretization that preserves the geometrical structure, i.e. the Dirac structure, underlying 2D heat and wave equations in cylindrical coordinates. These equations are shown to rely on Dirac structures for a particular set of boundary conditions. The discretization is completed with time integration based on Stormer-Verlet method.

Keywords

Distributed port-Hamiltonian systems; staggered grids; finite difference method; wave equation; heat equation

Citation

• Journal: IFAC-PapersOnLine
• Year: 2018
• Volume: 51
• Issue: 2
• Pages: 571–576
• Publisher: Elsevier BV
• DOI: 10.1016/j.ifacol.2018.03.096
• Note: 9th Vienna International Conference on Mathematical Modelling

BibTeX

@article{Trenchant_2018,
  title={{Structure Preserving Finite Differences in Polar Coordinates for Heat and Wave Equations.}},
  volume={51},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2018.03.096},
  number={2},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Trenchant, Vincent and Hu, Weiwei and Ramirez, Hector and Gorrec, Yann Le},
  year={2018},
  pages={571--576}
}

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References

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