Explicit structure-preserving discretization of port-Hamiltonian systems with mixed boundary control

Andrea Brugnoli; Ghislain Haine; Denis Matignon

doi:10.1016/j.ifacol.2022.11.089

Explicit structure-preserving discretization of port-Hamiltonian systems with mixed boundary control

Andrea Brugnoli
, Ghislain Haine
, Denis Matignon

Research output: Contribution to journal › Conference article › Academic › peer-review

9 Citations (Scopus)

161 Downloads (Pure)

Abstract

In this contribution, port-Hamiltonian systems with non-homogeneous mixed boundary conditions are discretized in a structure-preserving fashion by means of the Partitioned FEM. This means that the power balance and the port-Hamiltonian structure of the continuous equations is preserved at the discrete level. The general construction relies on a weak imposition of the boundary conditions by means of the Hellinger-Reissner variational principle, as recently proposed in [Thoma et al., 2021]. The case of linear hyperbolic wave-like systems, including the elastodynamic problem and the Maxwell equations in 3D, is then illustrated in detail. A numerical example is worked out on the case of the wave equation.

Original language	English
Pages (from-to)	418-423
Number of pages	6
Journal	IFAC-papersonline
Volume	55
Issue number	30
DOIs	https://doi.org/10.1016/j.ifacol.2022.11.089
Publication status	Published - 23 Nov 2022
Event	25th international conference on Mathematical Theory of Networks and Systems, MTNS 2022 - University of Bayreuth, Bayreuth, Germany Duration: 12 Sept 2022 → 16 Sept 2022 Conference number: 25

Keywords

Mixed Boundary Control
Partitioned Finite Element Method (PFEM)
Port-Hamiltonian systems (pHs)

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10.1016/j.ifacol.2022.11.089Licence: CC BY-NC-ND

1-s2.0-S2405896322027227-mainFinal published version, 509 KBLicence: CC BY-NC-ND

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title = "Explicit structure-preserving discretization of port-Hamiltonian systems with mixed boundary control",

abstract = "In this contribution, port-Hamiltonian systems with non-homogeneous mixed boundary conditions are discretized in a structure-preserving fashion by means of the Partitioned FEM. This means that the power balance and the port-Hamiltonian structure of the continuous equations is preserved at the discrete level. The general construction relies on a weak imposition of the boundary conditions by means of the Hellinger-Reissner variational principle, as recently proposed in [Thoma et al., 2021]. The case of linear hyperbolic wave-like systems, including the elastodynamic problem and the Maxwell equations in 3D, is then illustrated in detail. A numerical example is worked out on the case of the wave equation.",

keywords = "Mixed Boundary Control, Partitioned Finite Element Method (PFEM), Port-Hamiltonian systems (pHs)",

author = "Andrea Brugnoli and Ghislain Haine and Denis Matignon",

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T1 - Explicit structure-preserving discretization of port-Hamiltonian systems with mixed boundary control

AU - Brugnoli, Andrea

AU - Haine, Ghislain

AU - Matignon, Denis

N1 - Conference code: 25

PY - 2022/11/23

Y1 - 2022/11/23

N2 - In this contribution, port-Hamiltonian systems with non-homogeneous mixed boundary conditions are discretized in a structure-preserving fashion by means of the Partitioned FEM. This means that the power balance and the port-Hamiltonian structure of the continuous equations is preserved at the discrete level. The general construction relies on a weak imposition of the boundary conditions by means of the Hellinger-Reissner variational principle, as recently proposed in [Thoma et al., 2021]. The case of linear hyperbolic wave-like systems, including the elastodynamic problem and the Maxwell equations in 3D, is then illustrated in detail. A numerical example is worked out on the case of the wave equation.

AB - In this contribution, port-Hamiltonian systems with non-homogeneous mixed boundary conditions are discretized in a structure-preserving fashion by means of the Partitioned FEM. This means that the power balance and the port-Hamiltonian structure of the continuous equations is preserved at the discrete level. The general construction relies on a weak imposition of the boundary conditions by means of the Hellinger-Reissner variational principle, as recently proposed in [Thoma et al., 2021]. The case of linear hyperbolic wave-like systems, including the elastodynamic problem and the Maxwell equations in 3D, is then illustrated in detail. A numerical example is worked out on the case of the wave equation.

KW - Mixed Boundary Control

KW - Partitioned Finite Element Method (PFEM)

KW - Port-Hamiltonian systems (pHs)

UR - https://www.scopus.com/pages/publications/85144820963

U2 - 10.1016/j.ifacol.2022.11.089

DO - 10.1016/j.ifacol.2022.11.089

M3 - Conference article

AN - SCOPUS:85144820963

SN - 2405-8963

VL - 55

SP - 418

EP - 423

JO - IFAC-papersonline

JF - IFAC-papersonline

IS - 30

T2 - 25th international conference on Mathematical Theory of Networks and Systems, MTNS 2022

Y2 - 12 September 2022 through 16 September 2022

ER -

Explicit structure-preserving discretization of port-Hamiltonian systems with mixed boundary control

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Keywords

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