No Cover Image

Journal article 212 views 44 downloads

Non-intrusive reduced order modelling with least squares fitting on a sparse grid / Z. Lin, D. Xiao, F. Fang, C. C. Pain, Ionel M. Navon, Dunhui Xiao

International Journal for Numerical Methods in Fluids, Volume: 83, Issue: 3, Pages: 291 - 306

Swansea University Author: Dunhui Xiao

Check full text

DOI (Published version): 10.1002/fld.4268

Abstract

This paper presents a non‐intrusive reduced order model for general, dynamic partial differential equations. Based upon proper orthogonal decomposition (POD) and Smolyak sparse grid collocation, the method first projects the unknowns with full space and time coordinates onto a reduced POD basis. The...

Full description

Published in: International Journal for Numerical Methods in Fluids
ISSN: 0271-2091
Published: 2017
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa46453
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract: This paper presents a non‐intrusive reduced order model for general, dynamic partial differential equations. Based upon proper orthogonal decomposition (POD) and Smolyak sparse grid collocation, the method first projects the unknowns with full space and time coordinates onto a reduced POD basis. Then we introduce a new least squares fitting procedure to approximate the dynamical transition of the POD coefficients between subsequent time steps, taking only a set of full model solution snapshots as the training data during the construction. Thus, neither the physical details nor further numerical simulations of the original PDE model are required by this methodology, and the level of non‐intrusiveness is improved compared with existing reduced order models. Furthermore, we take adaptive measures to address the instability issue arising from reduced order iterations of the POD coefficients. This model can be applied to a wide range of physical and engineering scenarios, and we test it on a couple of problems in fluid dynamics. It is demonstrated that this reduced order approach captures the dominant features of the high‐fidelity models with reasonable accuracy while the computation complexity is reduced by several orders of magnitude.
Issue: 3
Start Page: 291
End Page: 306