Partitioned finite element method for structured discretization with mixed boundary conditions
Authors
Andrea Brugnoli, Flávio Luiz Cardoso-Ribeiro, Ghislain Haine, Paul Kotyczka
Abstract
The propagation of acoustic waves in a 2D geometrical domain under mixed boundary control is here described by means of the port-Hamiltonian (pH) formalism. A finite element based method is employed to obtain a consistently discretized model. To construct a model with mixed boundary control, two different methodologies are detailed: one employs Lagrange multipliers, the other relies on a virtual domain decomposition to interconnect models with different causalities. The two approaches are assessed numerically, by comparing the Hamiltonian and the state variables norm for progressively refined meshes.
Keywords
Aeroacoustics; port-Hamiltonian systems (pHs); Partitioned Finite Element Method (PFEM); Mixed Boundary Control
Citation
- Journal: IFAC-PapersOnLine
- Year: 2020
- Volume: 53
- Issue: 2
- Pages: 7557–7562
- Publisher: Elsevier BV
- DOI: 10.1016/j.ifacol.2020.12.1351
- Note: 21st IFAC World Congress- Berlin, Germany, 11–17 July 2020
BibTeX
@article{Brugnoli_2020,
title={{Partitioned finite element method for structured discretization with mixed boundary conditions}},
volume={53},
ISSN={2405-8963},
DOI={10.1016/j.ifacol.2020.12.1351},
number={2},
journal={IFAC-PapersOnLine},
publisher={Elsevier BV},
author={Brugnoli, Andrea and Cardoso-Ribeiro, Flávio Luiz and Haine, Ghislain and Kotyczka, Paul},
year={2020},
pages={7557--7562}
}References
- Beattie, C., Mehrmann, V., Xu, H. & Zwart, H. Linear port-Hamiltonian descriptor systems. Mathematics of Control, Signals, and Systems vol. 30 (2018) – 10.1007/s00498-018-0223-3
- Cardoso-Ribeiro, F. L., Matignon, D. & Lefèvre, L. A partitioned finite element method for power-preserving discretization of open systems of conservation laws. IMA Journal of Mathematical Control and Information vol. 38 493–533 (2020) – 10.1093/imamci/dnaa038
- Duindam, (2009)
- Gatica, (2014)
- Grisvard, P. Elliptic Problems in Nonsmooth Domains. (2011) doi:10.1137/1.9781611972030 – 10.1137/1.9781611972030
- Jacob, (2012)
- Kotyczka, P., Maschke, B. & Lefèvre, L. Weak form of Stokes–Dirac structures and geometric discretization of port-Hamiltonian systems. Journal of Computational Physics vol. 361 442–476 (2018) – 10.1016/j.jcp.2018.02.006
- Logg, (2012)
- Moulla, R., Lefévre, L. & Maschke, B. Pseudo-spectral methods for the spatial symplectic reduction of open systems of conservation laws. Journal of Computational Physics vol. 231 1272–1292 (2012) – 10.1016/j.jcp.2011.10.008
- Serhani, A., Haine, G. & Matignon, D. Anisotropic heterogeneous n-D heat equation with boundary control and observation: I. Modeling as port-Hamiltonian system. IFAC-PapersOnLine vol. 52 51–56 (2019) – 10.1016/j.ifacol.2019.07.009
- Serhani, A., Haine, G. & Matignon, D. Anisotropic heterogeneous n-D heat equation with boundary control and observation: II. Structure-preserving discretization. IFAC-PapersOnLine vol. 52 57–62 (2019) – 10.1016/j.ifacol.2019.07.010
- Trenchant, V., Ramirez, H., Le Gorrec, Y. & Kotyczka, P. Finite differences on staggered grids preserving the port-Hamiltonian structure with application to an acoustic duct. Journal of Computational Physics vol. 373 673–697 (2018) – 10.1016/j.jcp.2018.06.051
- van der Schaft, A. J. & Maschke, B. M. Hamiltonian formulation of distributed-parameter systems with boundary energy flow. Journal of Geometry and Physics vol. 42 166–194 (2002) – 10.1016/s0393-0440(01)00083-3
- Wu, Y., Hamroun, B., Gorrec, Y. L. & Maschke, B. Power preserving model reduction of 2D vibro-acoustic system: A port Hamiltonian approach. IFAC-PapersOnLine vol. 48 206–211 (2015) – 10.1016/j.ifacol.2015.10.240