Volume 57, Number 1, January-February 2023
|Page(s)||167 - 189|
|Published online||19 January 2023|
Stable model reduction for linear variational inequalities with parameter-dependent constraints
EDF R&D, 7 Boulevard Gaspard Monge, 91120 Palaiseau, France
2 CERMICS, École des Ponts, 6–8 avenue Blaise Pascal, 77455 Marne-la-Vallée cedex 2, France
3 INRIA Paris, 002 Rue Simone Iff, 75012 Paris, France
Accepted: 9 September 2022
We consider model reduction for linear variational inequalities with parameter-dependent 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 parameter-dependent 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-disks with parameter-dependent radius and on the membrane obstacle problem with parameter-dependent obstacle geometry.
Mathematics Subject Classification: 65N12 / 65N22 / 74S05 / 74M15
Key words: Model reduction / variational inequalities / reduced basis method / contact problem / obstacle problem / inf-sup condition
© The authors. Published by EDP Sciences, SMAI 2023
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