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

TL;DR

This paper introduces an adaptive model order reduction method that combines POD techniques with Newton-Krylov solvers to efficiently handle highly nonlinear mechanical problems with topological changes.

Contribution

It presents a novel algorithm that adaptively corrects reduced models in real-time, improving accuracy for problems with strong nonlinearities and topological changes.

Findings

Enhanced reduced order models with significant accuracy improvements

Effective correction method for damage initiation problems

Maintains computational efficiency despite complex nonlinearities

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.