Prud'homme, C;
Rovas, DV;
Veroy, K;
Machiels, L;
Maday, Y;
Patera, AT;
Turinici, G;
(2002)
Reliable real-time solution of parametrized partial differential equations: Reduced-basis output bound methods.
Journal of Fluids Engineering, Transactions of the ASME
, 124
(1)
pp. 70-80.
10.1115/1.1448332.
Text
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Abstract
We present a technique for the rapid and reliable prediction of linear-functional outputs of elliptic (and parabolic) partial differential equations with affine parameter dependence. The essential components are (i) (provably) rapidly convergent global reduced-basis approximations—Galerkin projection onto a space WN spanned by solutions of the governing partial differential equation at N selected points in parameter space; (ii) a posteriori error estimation—relaxations of the error-residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs of interest; and (iii) off-line/ on-line computational procedures methods which decouple the generation and projection stages of the approximation process. The operation count for the on-line stage in which, given a new parameter value, we calculate the output of interest and associated error bound, depends only on N (typically very small) and the parametric complexity of the problem; the method is thus ideally suited for the repeated and rapid evaluations required in the context of parameter estimation, design, optimization, and real-time control.
Type: | Article |
---|---|
Title: | Reliable real-time solution of parametrized partial differential equations: Reduced-basis output bound methods |
DOI: | 10.1115/1.1448332 |
Publisher version: | https://doi.org/10.1115/1.1448332 |
Language: | English |
UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of the Built Environment UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of the Built Environment > Bartlett School Env, Energy and Resources |
URI: | https://discovery.ucl.ac.uk/id/eprint/10063070 |
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