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Numerics for Physics-Based PDEs with Boundary Control: the Partitioned Finite Element Method for Port-Hamiltonian Systems

Brugnoli, Andrea and Matignon, Denis and Haine, Ghislain and Serhani, Anass Numerics for Physics-Based PDEs with Boundary Control: the Partitioned Finite Element Method for Port-Hamiltonian Systems. (2021) In: SIAM Conference on Computational Science and Engineering (CSE21), 1 March 2021 - 5 March 2021 (Virtual conference, Unknown).

(Document in English)

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The numerical simulation of complex open multiphysics systems in Computational Science and Engineering is a challenging topic. Based on energy exchanges, the port-Hamiltonian formalism aims at describing physics in a structured manner. One of the major interests of this approach is its versatility, allowing for coupling and interconnection that preserve this structure. We propose a Finite Element based technique for the structure-preserving discretization of a large class of port-Hamiltonian systems. Assuming a partitioned structure of the system associated to an integration-by-parts formula, it is possible to derive a consistent weak-formulation sharing the main features of the original boundary-controlled PDE. This allows using Galerkin approximations to obtain finite-dimensional systems that mimic the properties of the original distributed ones: the Partitioned Finite Element Method producing sparse matrices enables the use of dedicated algorithms in scientific computing. Indeed, this method can be easily implemented using well-established and robust libraries. This strategy is illustrated by means of physically motivated PDEs: acoustic waves, Mindlin and Kirchhoff plates, heat equation, Maxwell's equation. Interactive Jupyter notebooks are available, relying on the FEniCS open-source software. Advanced applications include multiphysics problems, e.g. fluid-structure interactions, thermoelasticity, and modular modelling of complex systems, e.g. multibody dynamics.

Item Type:Invited Conference
Audience (conference):International conference without published proceedings
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
Other partners > Institut national des sciences de l'Univers - INSU (FRANCE)
Laboratory name:
Deposited On:20 Sep 2021 14:02

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