| Issue |
ESAIM: M2AN
Volume 57, Number 1, January-February 2023
|
|
|---|---|---|
| Page(s) | 167 - 189 | |
| DOI | https://doi.org/10.1051/m2an/2022077 | |
| Published online | 19 January 2023 | |
Stable model reduction for linear variational inequalities with parameter-dependent constraints
1
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
* Corresponding author: idrissa.niakh@enpc.fr; niakhrek20@gmail.com
Received:
17
March
2022
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
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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