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

By C. Audouze, F. De Vuyst and P.B. Nair

Abstract

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

Topics: TA
Year: 2009
OAI identifier: oai:eprints.soton.ac.uk:71993
Provided by: e-Prints Soton
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