A structure-preserving Partitioned Finite Element Method for the 2D wave equation.
Authors
Flávio Luiz Cardoso-Ribeiro, Denis Matignon, Laurent Lefèvre
Abstract
Discretizing open systems of conservation laws while preserving the power-balance at the discrete level can be achieved using a new Partitioned Finite Element Method (PFEM), where an integration by parts is performed only on a subset of the variables in the weak formulation. Moreover, since boundary control and observation appear naturally in this formulation, the method is suitable both for simulation and control of infinite-dimensional port-Hamiltonian systems. The method can be applied using FEM software, and comes along with worked-out test cases on the 2D wave equation in different geometries and coordinate systems.
Keywords
Distributed Parameter systems; Port-Hamiltonian systems; Finite Element Method; Geometric Discretization Methods; 2D Wave equation
Citation
- Journal: IFAC-PapersOnLine
- Year: 2018
- Volume: 51
- Issue: 3
- Pages: 119–124
- Publisher: Elsevier BV
- DOI: 10.1016/j.ifacol.2018.06.033
- Note: 6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2018
BibTeX
@article{Cardoso_Ribeiro_2018,
title={{A structure-preserving Partitioned Finite Element Method for the 2D wave equation}},
volume={51},
ISSN={2405-8963},
DOI={10.1016/j.ifacol.2018.06.033},
number={3},
journal={IFAC-PapersOnLine},
publisher={Elsevier BV},
author={Cardoso-Ribeiro, Flávio Luiz and Matignon, Denis and Lefèvre, Laurent},
year={2018},
pages={119--124}
}
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