Partitioned finite element method for structured discretization with mixed boundary conditions

Andrea Brugnoli (1) , Flávio Luiz Cardoso-Ribeiro (2) , Ghislain Haine (3) , Paul Kotyczka (4)

1 DCAS - Département Conception et conduite des véhicules Aéronautiques et Spatiaux
2 ITA - Instituto Tecnológico de Aeronáutica [São José dos Campos]
3 DISC - Département d'Ingénierie des Systèmes Complexes
4 TUM - Technische Universität Munchen - Technical University Munich - Université Technique de Munich

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.

Mots clés: Aeroacoustics; port-Hamiltonian systems (pHs); Partitioned Finite Element Method (PFEM); Mixed Boundary Control

Domaines: Mathématiques générales [math.GM]

Andrea Brugnoli, Flávio Luiz Cardoso-Ribeiro, Ghislain Haine, Paul Kotyczka. Partitioned finite element method for structured discretization with mixed boundary conditions. 21th IFAC World Congress -1st Virtual IFAC World Congress, Jul 2020, Berlin (virtual), Germany. pp.7557-7562, ⟨10.1016/j.ifacol.2020.12.1351⟩. ⟨hal-03202663⟩