Bridging Proper Orthogonal Decomposition methods and augmented Newton-Krylov algorithms: an adaptive model order reduction for highly nonlinear mechanical problems

Pierre Kerfriden (1) , Pierre Gosselet (2) , Sondipon Adhikari (3) , Stephane Pierre-Alain Bordas (1)

1 School of Engineering [Cardiff]
2 LMT - Laboratoire de Mécanique et Technologie
3 School of engineering

This article describes a bridge between POD-based model order reduction techniques and the classical Newton/Krylov solvers. This bridge is used to derive an efficient algorithm to correct, ''on-the-fly", the reduced order modelling of highly nonlinear problems undergoing strong topological changes. Damage initiation problems are addressed and tackle via a corrected hyperreduction method. It is shown that the relevancy of reduced order model can be significantly improved with reasonable additional costs when using this algorithm, even when strong topological changes are involved.

Mots clés: Model order reduction (MOR); Time-dependant nonlinear mechanical problems; Proper orthogonal decomposition (POD); Real-time simulations; Newton/Krylov Solver; Projected conjugate gradient; Hyperreduction; CH-POD; Damage propagation

Domaines: Mécanique des structures [physics.class-ph]; Mécanique des structures [physics.class-ph]

Pierre Kerfriden, Pierre Gosselet, Sondipon Adhikari, Stephane Pierre-Alain Bordas. Bridging Proper Orthogonal Decomposition methods and augmented Newton-Krylov algorithms: an adaptive model order reduction for highly nonlinear mechanical problems. Computer Methods in Applied Mechanics and Engineering, 2010, 200 (5-8), pp.850-866. ⟨10.1016/j.cma.2010.10.009⟩. ⟨hal-00537900⟩