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

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 a reduced integration domain (RID) is considered. basis restriction RID full-order basis, which ensures hyper-reduced model respect non-linearity constraints. However, verification solvability condition, associated with well-posedness solution, may induce an extension primal without guaranteeing accurate forces. We highlight strong link between condition number projected rigidity matrix and precision solutions. Two efficient strategies enrichment POD are then introduced. large parametric variation zone, reachable remain limited. clustering strategy space proposed in order deal piece-wise low-rank approximations. On each cluster, local built thanks strategies. overall solution deeply improved while preserving interesting compression both bases.