On nonlinear inverse problems of heat transfer with radiation boundary conditions : application to dehydratation of gypsum plasterboards exposed to fire.

Aziz Belmiloudi (1) , Fabrice Mahé (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

The paper investigates boundary optimal controls and parameter estimates to the well-posedness nonlinear model of dehydration of thermic problems. We summarize the general formulations for the boundary control for initial-boundary value problem for nonlinear partial differential equations modeling the heat transfer and derive necessary optimality conditions, including the adjoint equation, for the optimal set of parameters minimizing objective functions J. Numerical simulations illustrate several numerical optimization methods, examples, and realistic cases, in which several interesting phenomena are observed. A large amount of computational effort is required to solve the coupled state equation and the adjoint equation (which is backwards in time), and the algebraic gradient equation (which implements the coupling between the adjoint and control variables). The state and adjoint equations are solved using the finite element method.

Mots clés: Optimal control; model calibration; numerical approximation; control constraint; adjoint model; dehydratation of gypsum; Comsol; Matlab.; Matlab

Domaines: Optimisation et contrôle [math.OC]; Analyse numérique [math.NA]

Aziz Belmiloudi, Fabrice Mahé. On nonlinear inverse problems of heat transfer with radiation boundary conditions : application to dehydratation of gypsum plasterboards exposed to fire.. advances in numerical analysis, 2014, 2014, 18 p. ⟨10.1155/2014/634712⟩. ⟨hal-00681784v2⟩