Preconditioned least-squares Petrov–Galerkin reduced order models

Abstract

This work proposes a preconditioning strategy for the least-squares Petrov–Galerkin (LSPG) reduced-order model. Preconditioning is critical for ensuring that the LSPG method produces accurate reduced-order models, particularly when the full-order model exhibits disparate scales or units across different components of the state vector. We analyze the effect of preconditioning on the LSPG formulation and demonstrate that appropriate preconditioning can significantly improve the accuracy and stability of the resulting reduced-order models.

Publication
International Journal for Numerical Methods in Engineering, 123(20):4809–4843, 2022

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