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arXiv · 2501.01621

A hyperreduced reduced basis element method for reduced-order modeling of component-based nonlinear systems

Mehran Ebrahimi·Masayuki Yano
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Abstract

We introduce a hyperreduced reduced basis element method for model reduction of parameterized, component-based systems in continuum mechanics governed by nonlinear partial differential equations. In the offline phase, the method constructs, through a component-wise empirical training, a library of archetype components defined by a component-wise reduced basis and hyperreduced quadrature rules with varying hyperreduction fidelities. In the online phase, the method applies an online adaptive scheme informed by the Brezzi-Rappaz-Raviart theorem to select an appropriate hyperreduction fidelity for each component to meet the user-prescribed error tolerance at the system level. The method accommodates the rapid construction of hyperreduced models for large-scale component-based nonlinear systems and enables model reduction of problems with many continuous and topology-varying parameters. The efficacy of the method is demonstrated on a two-dimensional nonlinear thermal fin system that comprises up to 225 components and 68 independent parameters.

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Mehran Ebrahimi, Masayuki Yano. 2025-01-03. A hyperreduced reduced basis element method for reduced-order modeling of component-based nonlinear systems. https://doi.org/10.1016/j.cma.2024.117254

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