Goal-oriented time adaptivity for port-Hamiltonian systems

Authors

Andreas Bartel, Manuel Schaller

Abstract

Port-Hamiltonian systems provide an energy-based modeling paradigm for dynamical input-state-output systems. At their core, they fulfill an energy balance relating stored, dissipated and supplied energy. To accurately resolve this energy balance in time discretizations, we propose an adaptive grid refinement technique based on a posteriori error estimation. The evaluation of the error estimator includes the computation of adjoint sensitivities. To interpret this adjoint equation as a backwards-in-time equation, we show piecewise weak differentiability of the dual variable. Then, leveraging dissipativity of the port-Hamiltonian dynamics, we present a parallelizable approximation of the underlying adjoint system in the spirit of a block-Jacobi method to efficiently compute error indicators. We illustrate the performance of the proposed scheme by means of numerical experiments showing that it yields a smaller violation of the energy balance when compared to uniform refinements and traditional step size controlled time stepping.

Keywords

Goal-oriented grid adaptivity; Port-Hamiltonian systems; Energy balance

Citation

• Journal: Journal of Computational and Applied Mathematics
• Year: 2025
• Volume: 461
• Issue:
• Pages: 116450
• Publisher: Elsevier BV
• DOI: 10.1016/j.cam.2024.116450

BibTeX

@article{Bartel_2025,
  title={{Goal-oriented time adaptivity for port-Hamiltonian systems}},
  volume={461},
  ISSN={0377-0427},
  DOI={10.1016/j.cam.2024.116450},
  journal={Journal of Computational and Applied Mathematics},
  publisher={Elsevier BV},
  author={Bartel, Andreas and Schaller, Manuel},
  year={2025},
  pages={116450}
}

Download the bib file

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