title: Bridging Proper Orthogonal Decomposition methods and augmented Newton-Krylov algorithms: an adaptive model order reduction for highly nonlinear mechanical problems.
abstract: 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.
authors.affiliation: Cardiff University, Queen's Buildings, The Parade, Cardiff CF24 3AA, Wales, UK.
authors.forename: P
authors.initials: P
authors.lastname: Kerfriden
authors.affiliation: Ecole Normale Superieure de Cachan, 61 Avenue du Président Wilson, F-94230 Cachan, France.
authors.forename: P
authors.initials: P
authors.lastname: Gosselet
authors.affiliation: Swansea University, Singleton Park, Swansea, SA2 8PP, Wales UK.
authors.forename: S
authors.initials: S
authors.lastname: Adhikari
authors.affiliation: Cardiff University, Queen's Buildings, The Parade, Cardiff CF24 3AA, Wales, UK.
authors.forename: S
authors.initials: S
authors.lastname: Bordas
keywords: CH-POD; Damage propagation; Hyperreduction; Model order reduction (MOR); Newton/Krylov Solver; Projected conjugate gradient; Proper orthogonal decomposition (POD); System approximation; Time-dependant nonlinear mechanical problems