Numerical approximation of port-Hamiltonian systems for hyperbolic or parabolic PDEs with boundary control
| Autor: | Anass Serhani, Ghislain Haine, Xavier Vasseur, Andrea Brugnoli |
|---|---|
| Přispěvatelé: | Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE), Centre Européen de Recherche et Formation Avancées en Calcul Scientifique - CERFACS (FRANCE), University of Twente (NETHERLANDS), Département d'Ingénierie des Systèmes Complexes - DISC (Toulouse, France), University of Twente [Netherlands], Département d'Ingénierie des Systèmes Complexes (DISC), Institut Supérieur de l'Aéronautique et de l'Espace (ISAE-SUPAERO), Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique (CERFACS), CERFACS |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
[SPI.OTHER]Engineering Sciences [physics]/Other
0209 industrial biotechnology Discretization Port-Hamiltonian Systems Computer science 65M60 35L90 35K90 Boundary (topology) 010103 numerical & computational mathematics 02 engineering and technology Dynamical Systems (math.DS) 01 natural sciences Hamiltonian system 020901 industrial engineering & automation Autre FOS: Mathematics Applied mathematics Mathematics - Numerical Analysis 0101 mathematics Mathematics - Dynamical Systems Boundary Control Structure-Preserving Discretization Partial differential equation Computer simulation Partial Differential Equations Partial Differential Equations Boundary Control General Medicine Numerical Analysis (math.NA) Wave equation Finite element method Finite Element Method Heat equation |
| Zdroj: | Journal of Applied Mathematics and Physics (JAMP) Journal of Applied Mathematics and Physics (JAMP), Scientific Research Publishing, 2021, 09 (06), pp.1278-1321. ⟨10.4236/jamp.2021.96088⟩ |
| ISSN: | 2327-4352 |
| Popis: | We consider the design of structure-preserving discretization methods for the solution of systems of boundary controlled Partial Differential Equations (PDEs) thanks to the port-Hamiltonian formalism. We first provide a novel general structure of infinite-dimensional port-Hamiltonian systems (pHs) for which the Partitioned Finite Element Method (PFEM) straightforwardly applies. The proposed strategy is applied to abstract multidimensional linear hyperbolic and parabolic systems of PDEs. Then we show that instructional model problems based on the wave equation, Mindlin equation and heat equation fit within this unified framework. Secondly we introduce the ongoing project SCRIMP (Simulation and ContRol of Interactions in Multi-Physics) developed for the numerical simulation of infinite-dimensional pHs. SCRIMP notably relies on the FEniCS open-source computing platform for the finite element spatial discretization. Finally, we illustrate how to solve the considered model problems within this framework by carefully explaining the methodology. As additional support, companion interactive Jupyter notebooks are available. 33 pages |
| Databáze: | OpenAIRE |
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