Premium
A reduced basis method for parametrized variational inequalities applied to contact mechanics
Author(s) -
Benaceur Amina,
Ern Alexandre,
Ehrlacher Virginie
Publication year - 2019
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6261
Subject(s) - basis (linear algebra) , mathematics , lagrange multiplier , interpolation (computer graphics) , saddle point , nonlinear system , reduction (mathematics) , polygon mesh , mathematical optimization , constraint (computer aided design) , constraint algorithm , dual (grammatical number) , computer science , geometry , frame (networking) , physics , art , telecommunications , literature , quantum mechanics
Summary We investigate new developments of the reduced‐basis 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 nonmatching meshes. The numerical examples confirm the efficiency of the reduction strategy.