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

Abstract : 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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https://hal.archives-ouvertes.fr/hal-02081485
Contributor : Amina Benaceur <>
Submitted on : Wednesday, March 27, 2019 - 6:19:03 PM
Last modification on : Monday, April 8, 2019 - 6:56:52 PM

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  • HAL Id : hal-02081485, version 2

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Amina Benaceur, Alexandre Ern, Virginie Ehrlacher. A reduced basis method for parametrized variational inequalities applied to contact mechanics. 2019. ⟨hal-02081485v2⟩

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