Bridging Proper Orthogonal Decomposition methods and augmented   Newton-Krylov algorithms: an adaptive model order reduction for highly   nonlinear mechanical problems
  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. 
Pierre Kerfriden, Pierre Gosselet (LMT), Sondipon Adhikari, St\'ephane   Bordas
physics.class-ph physics.comp-ph