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Reduced order modelling of parameter dependent linear and nonlinear dynamic PDE models
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Shah, Akeel A., Xing, W. W. and Triantafyllidis, Vasileios (2017) Reduced order modelling of parameter dependent linear and nonlinear dynamic PDE models. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 473 (2200). 20160809. doi:10.1098/rspa.2016.0809 ISSN 1364-5021.
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Official URL: https://doi.org/10.1098/rspa.2016.0809
Abstract
In this paper we develop reduced-order models (ROMs) for dynamic, parameter-dependent, linear and nonlinear partial differential equations using proper orthogonal decomposition (POD). The main challenges are to accurately and efficiently approximate the POD bases for new parameter values and, in the case of nonlinear problems, to efficiently handle the nonlinear terms. We use a Bayesian nonlinear regression approach to learn the snapshots of the solutions and the nonlinearities for new parameter values. Computational efficiency is ensured by using manifold learning to perform the emulation in a low-dimensional space. The accuracy of the method is demonstrated on a linear and a nonlinear example, with comparisons to a global basis approach.
Item Type: | Journal Article | ||||||
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Subjects: | Q Science > QA Mathematics | ||||||
Divisions: | Faculty of Science, Engineering and Medicine > Engineering > Engineering | ||||||
Library of Congress Subject Headings (LCSH): | Differential equations, Partial -- Mathematical models, Gaussian processes | ||||||
Journal or Publication Title: | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences | ||||||
Publisher: | The Royal Society Publishing | ||||||
ISSN: | 1364-5021 | ||||||
Official Date: | 26 April 2017 | ||||||
Dates: |
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Volume: | 473 | ||||||
Number: | 2200 | ||||||
Article Number: | 20160809 | ||||||
DOI: | 10.1098/rspa.2016.0809 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||
Date of first compliant deposit: | 25 September 2017 | ||||||
Date of first compliant Open Access: | 27 September 2017 | ||||||
Funder: | Engineering and Physical Sciences Research Council (EPSRC), China Scholarship Council (CSC) | ||||||
Grant number: | EP/L027682/1, EP/P012620/1 and EP/L018330/1 | ||||||
Open Access Version: |
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