Anisotropic heterogeneous n-D heat equation with boundary control and observation : II. Structure-preserving discretization

Anass Serhani (1) , Ghislain Haine (1) , Denis Matignon (1)

1 DISC - Département d'Ingénierie des Systèmes Complexes

The heat equation with boundary control and observation can be described by means of three different Hamiltonians, the internal energy, the entropy, or a classical Lyapunov functional, as shown in the companion paper (Serhani et al. (2019a)). The aim of this work is to apply the partitioned finite element method (PFEM) proposed in Cardoso-Ribeiro et al. (2018) to the three associated port-Hamiltonian systems. Differential Algebraic Equations are obtained. The strategy proves very efficient to mimic the continuous Stokes-Dirac structure at the discrete level, and especially preserving the associated power balance. Anisotropic and heterogeneous 2D simulations are finally performed on the Lyapunov formulation to provide numerical evidence that this strategy proves very efficient for the accurate simulation of a boundary controlled and observed infinite-dimensional system.

Mots clés: Port-Hamiltonian Differential Algebraic System; Heat Equation; Structure Preserving Discretization; Partitionned Finite Element Method (PFEM); Boundary Control

Domaines: Systèmes dynamiques [math.DS]

Anass Serhani, Ghislain Haine, Denis Matignon. Anisotropic heterogeneous n-D heat equation with boundary control and observation : II. Structure-preserving discretization. 3rd IFAC Workshop on Thermodynamic Foundations for a Mathematical Systems Theory (TFMST 2019), Jul 2019, Louvain-la-Neuve, Belgium. pp.57-62, ⟨10.1016/j.ifacol.2019.07.010⟩. ⟨hal-02278354⟩