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Institutional Repository [SANDBOX]
Technical University of Crete
Technical University of Crete
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| URI: | http://purl.tuc.gr/dl/dias/18E74415-545E-4E65-AF59-D88EF61C2CB5 | ||
| Year | 2001 | ||
| Type of Item | Peer-Reviewed Journal Publication | ||
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| Bibliographic Citation | C. Prud’homme, D.V. Rovas, K. Veroy, L. Machiels, Y. Maday, A.T. Patera, "Reliable real-time solution of parametrized partial differential equations: Reduced-basis output bound methods," J. of Fluids Eng. ,vol.124 ,no.1,pp. 70-80,2001.doi:10.1115/1.1448332 https://doi.org/10.1115/1.1448332 | ||
| Appears in Collections |
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 gov- erning partial differential equation at N selected points in parameter space; (ii) a poste- riori 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 contro
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