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Journal Articles ESAIM: Mathematical Modelling and Numerical Analysis Year : 2023

Stable model reduction for linear variational inequalities with parameter-dependent constraints

Abstract

We consider model reduction for linear variational inequalities with parameterdependent constraints. We study the stability of the reduced problem in the context of a dualized formulation of the constraints using Lagrange multipliers. Our main result is an algorithm that guarantees inf-sup stability of the reduced problem. The algorithm is computationally effective since it can be performed in the offline phase even for parameterdependent constraints. Moreover, we also propose a modification of the Cone Projected Greedy algorithm so as to avoid ill-conditioning issues when manipulating the reduced dual basis. Our results are illustrated numerically on the frictionless Hertz contact problem between two half-spheres with parameter-dependent radius and on the membrane obstacle problem with parameter-dependent obstacle geometry.
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Dates and versions

hal-03611982 , version 1 (17-03-2022)
hal-03611982 , version 2 (06-09-2022)
hal-03611982 , version 3 (12-09-2022)

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Idrissa Niakh, Guillaume Drouet, Virginie Ehrlacher, Alexandre Ern. Stable model reduction for linear variational inequalities with parameter-dependent constraints. ESAIM: Mathematical Modelling and Numerical Analysis, 2023, 57 (1), pp.167--189. ⟨10.1051/m2an/2022077⟩. ⟨hal-03611982v3⟩
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