Advancing industrial finite element software: Developing Model Order Reduction for nonlinear transient thermal problems

Abstract

Over the past two decades, non-intrusive techniques have been used to develop reduced-order models for nonlinear structures in industrial environments. These techniques have placed a significant emphasis on a posteriori methods, which often rely on solutions derived from computationally expensive full-order models. Using a priori methods not relying on the full order model might be preferred as they reduce the computational burden upfront. The intrusiveness of the algorithms associated with these methods limits their introduction into commercial finite element software. Integrating robust and reliable approaches into a certified product is necessary for these methods to spread at an industrial level. This work aligns with this ambition, extending a weakly-intrusive implementation of the LATIN-PGD already embedded into commercial finite element software to transient thermal problems. The novelty of the approach stems from its extensive applicability, enabling the PGD method to address not just specific applications but also to seamlessly handle any nonlinearities, diverse element types, various boundary conditions, and other features inherent in such software. This results in a new comprehensive industrial nonlinear solver, including a priori model order reduction.