A nonintrusive finite-orthogonal-basis reduced-order model for accelerated computation of geometrically parameterized problems

Accelerated computation of geometrically parameterized problems has become a key task in computational science and engineering. The hyper projection-based reduced order models (HPROMs) serve as essential physical tool for speeding up these computations. However, HPROMs require users to have intrusiv...

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Bibliographic Details
Published in:Engineering with computers Vol. 41; no. 5; pp. 3425 - 3450
Main Authors: Wang, Hongjiang, Qiao, Lijie, Dong, Han, Huang, Chaohui, Wang, Weizhe, Liu, Yingzheng
Format: Journal Article
Language:English
Published: London Springer London 01.10.2025
Springer Nature B.V
Subjects:
Approximation
Blood flow
Boundary conditions
CAE) and Design
Calculus of Variations and Optimal Control; Optimization
Channel flow
Classical Mechanics
Computation
Computer Science
Computer-Aided Engineering (CAD
Control
Data acquisition
Deformation
Differential equations
Finite volume method
Fluid dynamics
Geometry
Math. Applications in Chemistry
Mathematical and Computational Engineering
Numerical analysis
Operators (mathematics)
Original Article
Parameterization
Partial differential equations
Reduced order models
Software
Solid mechanics
Source code
Systems Theory
Geometrical parametrization
Hyper-reduction
Reduced-order models
Nonintrusive
ISSN:0177-0667, 1435-5663
Online Access:Get full text
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Summary:Accelerated computation of geometrically parameterized problems has become a key task in computational science and engineering. The hyper projection-based reduced order models (HPROMs) serve as essential physical tool for speeding up these computations. However, HPROMs require users to have intrusive access to the source code to collect the intrusive snapshots of nonlinear operators and to embed the projection and approximation processes within code. It’s challenging for most users of commercial software. Accordingly, we propose an innovative nonintrusive reduced-order methods including finite-orthogonal-basis geometrical-information reduced-order model (FBG-ROM) and its hyper-reduced form, finite-orthogonal-basis geometrical-information hyper-reduced-order model (FBG-HROM). These methods directly discretize PDEs via reduced order bases and its corresponding differential operator which implies the geometry deformation information, rather than via element-wise traversal used in PROMs and HPROMs. This discretizing approach gives FBG-HROM a nonintrusive characteristic in terms of model discretization during the online phase, allowing users of commercial software to discretize the PDEs without relying on numerical computation models that have a high barrier, and a nonintrusive characteristic in terms of data acquisition during the offline phase, allowing users to obtain all necessary snapshots through commercial software. We demonstrate the accelerated computations of the FBG-HROM on three classic cases of fluid dynamics and solid mechanics—curved channel flow, blood flow in a stenotic vessel, and a plate with a hole—highlighting the excellent generalization performance and acceleration effects of the proposed frameworks.
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ISSN:0177-0667
1435-5663
DOI:10.1007/s00366-025-02172-6