An Integrated Workflow for Solving Parametric Nonlinear Problems Through Reduced Order Modeling
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Reduced-order modeling methods, like Proper Orthogonal Decomposition (POD), Reduced Basis (RB), and Proper Generalized Decomposition (PGD), are well established in Mechanical engineering for their effectiveness in achieving efficient numerical simulations. Despite a high degree of maturity and a wide range of applications, integrating these methods into industrial environments faces challenges due to their intrusive formulations. Recently, Siemens has made progress by implementing ROM solutions natively in its Simcenter Samcef nonlinear structural solver. Using a weakly-intrusive reformulation of the method, the LATIN-PGD algorithm [1] was implemented as close as possible to the source code [2]. This work addresses a restrictive limitation by extending the weakly-intrusive formulation to transient behavior, focusing on thermal problems. The formulation, easily implementable in any general-purpose industrial finite element software, enables capitalization on all past developments and seamless integration of ROM methods in engineers’ workflows [3]. This work outlines the main ingredients needed to pair an industrial encapsulation of the LATIN-PGD with parametric exploration software. The implemented algorithm leverages specific features of the LATIN-PGD method: flexible initialization from a previous solution, re-use of computed bases, and multi-fidelity properties to yield an efficient parametric space exploration or optimization process. REFERENCES [1] P. Ladevèze, Nonlinear computational structural mechanics: new approaches and non-incremental methods of calculation. Springer Science & Business Media, 1999. [2] R. Scanff, D. Néron, P. Ladevèze, P. Barabinot, F. Cugnon, J.-P. Delsemme, Weakly-invasive LATIN-PGD for solving time-dependent non-linear parametrized problems in solid mechanics. Comput. Methods Appl. Mech. Engrg.,396, 114999, 2022. [3] P.-E. Malleval, R. Scanff, D. Néron, Solving nonlinear transient problems in an industrial code using a weakly-intrusive Model Order Reduction method, Article in preparation.