Bridging Proper Orthogonal Decomposition methods and augmented Newton-Krylov algorithms: an adaptive model order...

Area of Science:

• Computational mechanics
• Numerical analysis
• Model order reduction

Background:

• Model order reduction (MOR) techniques, such as Proper Orthogonal Decomposition (POD), are essential for efficiently simulating complex systems.
• Classical Newton/Krylov solvers are widely used for solving nonlinear problems but can be computationally expensive for large-scale simulations.
• Simulating highly nonlinear problems with strong topological changes, like damage initiation, poses significant challenges for traditional MOR and solvers.

Purpose of the Study:

• To develop an efficient algorithm that bridges POD-based model order reduction and Newton/Krylov solvers.
• To enable real-time correction of reduced-order models for highly nonlinear problems with significant topological changes.
• To improve the accuracy and relevance of reduced-order models in scenarios involving damage initiation.

Main Methods:

• A novel algorithm is derived by connecting POD-based model order reduction with Newton/Krylov solvers.
• The algorithm implements a corrected hyperreduction method to address problems with strong topological changes.
• The approach focuses on 'on-the-fly' correction of the reduced-order model during simulation.

Main Results:

• The proposed algorithm effectively corrects reduced-order models for highly nonlinear problems.
• Significant improvements in the relevancy of the reduced-order model are achieved.
• The method demonstrates efficacy even when dealing with strong topological changes, such as those in damage initiation problems.
• The accuracy enhancements come with reasonable additional computational costs.

Conclusions:

• The developed bridge between POD-based MOR and Newton/Krylov solvers offers an efficient solution for complex nonlinear simulations.
• The corrected hyperreduction method significantly enhances the performance of reduced-order models in the presence of topological changes.
• This approach provides a valuable tool for simulating phenomena like damage initiation with improved accuracy and efficiency.