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

TL;DR

This paper presents a hyperreduced reduced basis element method for efficient model reduction of large-scale, parameter-dependent nonlinear systems, enabling rapid and adaptive construction of accurate reduced models for complex component-based problems.

Contribution

It introduces a novel hyperreduced basis element approach with adaptive fidelity selection for component-based nonlinear systems, improving efficiency and scalability.

Findings

Effective reduction of a 225-component thermal fin system

Adaptive hyperreduction fidelity achieves prescribed error tolerances

Method handles many parameters and topology variations

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.