Accelerated construction of projection-based reduced-order models via incremental approaches

2024/01/13 by Eki Agouzal, Agouzal, Eki, Tommaso Taddei +1
Decision Sciences · Engineering · Physics and Astronomy · #FOS: Mathematics #Model Reduction and Neural Networks #Nuclear reactor physics and engineering #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design

paper · pdf · doi:10.48550/arxiv.2401.07108

openalex publication_date 2024/01/13 · openalex created_date 2024/01/18 · openalex updated_date 2026/07/28

Abstract

We present an accelerated greedy strategy for training of projection-based reduced-order models for parametric steady and unsteady partial differential equations. Our approach exploits hierarchical approximate proper orthogonal decomposition to speed up the construction of the empirical test space for least-square Petrov-Galerkin formulations, a progressive construction of the empirical quadrature rule based on a warm start of the non-negative least-square algorithm, and a two-fidelity sampling strategy to reduce the number of expensive greedy iterations. We illustrate the performance of our method for two test cases: a two-dimensional compressible inviscid flow past a LS89 blade at moderate Mach number, and a three-dimensional nonlinear mechanics problem to predict the long-time structural response of the standard section of a nuclear containment building under external loading.

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