A structure-preserving Partitioned Finite Element Method for the 2D wave equation

Flávio Luiz Cardoso-Ribeiro (1) , Denis Matignon (2) , Laurent Lefevre (3)

1 ITA - Instituto Tecnológico de Aeronáutica [São José dos Campos]
2 DISC - Département d'Ingénierie des Systèmes Complexes
3 LCIS - Laboratoire de Conception et d'Intégration des Systèmes

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.

Mots clés: Distributed Parameter systems; Port-Hamiltonian systems; Finite Element Method; Geometric Discretization Methods; 2D Wave equation

Domaines: Automatique / Robotique

Flávio Luiz Cardoso-Ribeiro, Denis Matignon, Laurent Lefevre. A structure-preserving Partitioned Finite Element Method for the 2D wave equation. 6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNLC 2018, May 2018, Valparaiso, Chile. ⟨10.1016/j.ifacol.2018.06.033⟩. ⟨hal-02074472⟩