Condition Number and Clustering-Based Efficiency Improvement of Reduced-Order Solvers for Contact Problems Using Lagrange Multipliers

Simon Le Berre, Isabelle Ramière, Jules Fauque and David Ryckelynck
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Simon Le Berre: CEA, DES, IRESNE, DEC, SESC, LSC, Cadarache, F-13108 Saint-Paul-Lez-Durance, France
Isabelle Ramière: CEA, DES, IRESNE, DEC, SESC, LSC, Cadarache, F-13108 Saint-Paul-Lez-Durance, France
Jules Fauque: CEA, DES, IRESNE, DEC, SESC, LSC, Cadarache, F-13108 Saint-Paul-Lez-Durance, France
David Ryckelynck: PSL Mines-ParisTech, Centre des Matériaux, F-91003 Evry, France

Mathematics, 2022, vol. 10, issue 9, 1-25

Abstract: This paper focuses on reduced-order modeling for contact mechanics problems treated by Lagrange multipliers. The high nonlinearity of the dual solutions lead to poor classical data compression. A hyper-reduction approach based on a reduced integration domain (RID) is considered. The dual reduced basis is the restriction to the RID of the full-order dual basis, which ensures the hyper-reduced model to respect the non-linearity constraints. However, the verification of the solvability condition, associated with the well-posedness of the solution, may induce an extension of the primal reduced basis without guaranteeing accurate dual forces. We highlight the strong link between the condition number of the projected contact rigidity matrix and the precision of the dual reduced solutions. Two efficient strategies of enrichment of the primal POD reduced basis are then introduced. However, for large parametric variation of the contact zone, the reachable dual precision may remain limited. A clustering strategy on the parametric space is then proposed in order to deal with piece-wise low-rank approximations. On each cluster, a local accurate hyper-reduced model is built thanks to the enrichment strategies. The overall solution is then deeply improved while preserving an interesting compression of both primal and dual bases.

Keywords: hyper-reduction; contact mechanics; Lagrange multipliers; solvability condition; condition number; clustering; local reduced order models (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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