The University of Southampton
University of Southampton Institutional Repository

Reduced-order modeling of parameterized PDEs using time-space-parameter principal component analysis

Reduced-order modeling of parameterized PDEs using time-space-parameter principal component analysis
Reduced-order modeling of parameterized PDEs using time-space-parameter principal component analysis
This paper presents a methodology for constructing low-order surrogate models of finite element/finite
volume discrete solutions of parameterized steady-state partial differential equations. The construction
of proper orthogonal decomposition modes in both physical space and parameter space allows us to
represent high-dimensional discrete solutions using only a few coefficients. An incremental greedy approach
is developed for efficiently tackling problems with high-dimensional parameter spaces. For numerical
experiments and validation, several non-linear steady-state convection–diffusion–reaction problems are
considered: first in one spatial dimension with two parameters, and then in two spatial dimensions with
two and five parameters. In the two-dimensional spatial case with two parameters, it is shown that a 7×7
coefficient matrix is sufficient to accurately reproduce the expected solution, while in the five parameters
problem, a 13×6 coefficient matrix is shown to reproduce the solution with sufficient accuracy. The
proposed methodology is expected to find applications to parameter variation studies, uncertainty analysis,
inverse problems and optimal design
metamodel, surrogate, reduced-order model (ROM), physics-based model, parameterized partial differential equation (PDE), radial basis functions (RBF), proper orthogonal decomposition (POD), design optimization, fluid dynamics problems
0029-5981
1025-1057
Audouze, C.
e71eb2b8-ac5c-40bb-bf37-d495d7c9bcb3
De Vuyst, F.
f25a6329-a551-405a-b6b4-56d32a6d2e3f
Nair, P.B.
d4d61705-bc97-478e-9e11-bcef6683afe7
Audouze, C.
e71eb2b8-ac5c-40bb-bf37-d495d7c9bcb3
De Vuyst, F.
f25a6329-a551-405a-b6b4-56d32a6d2e3f
Nair, P.B.
d4d61705-bc97-478e-9e11-bcef6683afe7

Audouze, C., De Vuyst, F. and Nair, P.B. (2009) Reduced-order modeling of parameterized PDEs using time-space-parameter principal component analysis. International Journal for Numerical Methods in Engineering, 80 (8), 1025-1057. (doi:10.1002/nme.2540).

Record type: Article

Abstract

This paper presents a methodology for constructing low-order surrogate models of finite element/finite
volume discrete solutions of parameterized steady-state partial differential equations. The construction
of proper orthogonal decomposition modes in both physical space and parameter space allows us to
represent high-dimensional discrete solutions using only a few coefficients. An incremental greedy approach
is developed for efficiently tackling problems with high-dimensional parameter spaces. For numerical
experiments and validation, several non-linear steady-state convection–diffusion–reaction problems are
considered: first in one spatial dimension with two parameters, and then in two spatial dimensions with
two and five parameters. In the two-dimensional spatial case with two parameters, it is shown that a 7×7
coefficient matrix is sufficient to accurately reproduce the expected solution, while in the five parameters
problem, a 13×6 coefficient matrix is shown to reproduce the solution with sufficient accuracy. The
proposed methodology is expected to find applications to parameter variation studies, uncertainty analysis,
inverse problems and optimal design

Text
Audo_10.pdf - Version of Record
Restricted to Repository staff only

More information

Submitted date: 14 February 2008
Published date: 20 November 2009
Keywords: metamodel, surrogate, reduced-order model (ROM), physics-based model, parameterized partial differential equation (PDE), radial basis functions (RBF), proper orthogonal decomposition (POD), design optimization, fluid dynamics problems

Identifiers

Local EPrints ID: 71993
URI: https://eprints.soton.ac.uk/id/eprint/71993
ISSN: 0029-5981
PURE UUID: 6af002ff-6f5d-4641-ba21-660fbc9d7dfe

Catalogue record

Date deposited: 14 Jan 2010
Last modified: 04 Nov 2019 21:08

Export record

Altmetrics

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of https://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×