A reduced basis method for parametrized variational inequalities applied to contact mechanics

Amina Benaceur (1, 2, 3) , Alexandre Ern (2, 3) , Virginie Ehrlacher (4, 2)

1 EDF - EDF
2 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
3 SERENA - Simulation for the Environment: Reliable and Efficient Numerical Algorithms
4 MATHERIALS - MATHematics for MatERIALS

We investigate new developments of the Reduced-Basis (RB) method for parametrized optimization problems with nonlinear constraints. We propose a reduced-basis scheme in a saddle-point form combined with the Empirical Interpolation Method to deal with the nonlinear constraint. In this setting, a primal reduced-basis is needed for the primal solution and a dual one is needed for the Lagrange multipliers. We suggest to construct the latter using a cone-projected greedy algorithm that conserves the non-negativity of the dual basis vectors. The reduction strategy is applied to elastic frictionless contact problems including the possibility of using non-matching meshes. The numerical examples confirm the efficiency of the reduction strategy.

Domaines: Analyse numérique [math.NA]; Mécanique des solides [physics.class-ph]

Amina Benaceur, Alexandre Ern, Virginie Ehrlacher. A reduced basis method for parametrized variational inequalities applied to contact mechanics. International Journal for Numerical Methods in Engineering, 2019, ⟨10.1002/nme.6261⟩. ⟨hal-02081485v3⟩