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Article Dans Une Revue International Journal for Numerical Methods in Engineering Année : 2019

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

Résumé

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.
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Dates et versions

hal-02081485 , version 1 (27-03-2019)
hal-02081485 , version 2 (27-03-2019)
hal-02081485 , version 3 (24-09-2019)

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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⟩
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