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An online-adaptive hyperreduced reduced basis element method for parameterized component-based nonlinear systems using hierarchical error estimation
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DOI：10.1016/j.cma.2025.118590.png)
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Abstract
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We present an online-adaptive hyperreduced reduced basis element method for model order reduction of parameterized, component-based nonlinear systems. The method, in the offline phase, prepares a library of hyperreduced archetype components of various fidelity levels and, in the online phase, assembles the target system using instantiated components whose fidelity is adaptively selected to satisfy a user-prescribed system-level error tolerance. To achieve this, we introduce a hierarchical error estimation framework that compares solutions at successive fidelity levels and drives a local refinement strategy based on component-wise error indicators. We also provide an efficient estimator for the system-level error to ensure that the adaptive strategy meets the desired accuracy. Component-wise hyperreduction is performed using an empirical quadrature procedure, with the training accuracy guided by the Brezzi–Rappaz–Raviart theorem. The proposed method is demonstrated on a family of nonlinear thermal fin systems comprising up to 225 components and 68 parameters. Numerical results show that the hyperreduced reduced basis element model achieves O(100) computational reduction at 1% error level relative to the truth finite-element model. In addition, the adaptive refinement strategy provides more effective error control than uniform refinement by selectively enriching components with higher local errors.
Keywords:
Component-based model order reduction
hyperreduced reduced basis element method
Brezzi–Rappaz–Raviart theorem
adaptive refinement
hierarchical error estimation
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