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An overview of blackbox reduced-basis output bound methods for elliptic partial differential equations

Rovas, D; (2000) An overview of blackbox reduced-basis output bound methods for elliptic partial differential equations. In: Deville, Michel and Owens, Robert, (eds.) Proceedings of 16th IMACS World Congress on Scientific Computation, Applied Mathematics and Simulation - 2000. IMACS: Lausanne, Switzerland. Green open access

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Abstract

We present a two-stage off-line/on-line blackbox reduced-basis output bound method for the prediction of outputs of interest of elliptic partial differential equations with affine parameter dependence. The computational complexity of the on-line stage of the procedure scales only with the dimension of the reduced-basis space and the parametric complexity of the partial differential operator. The method is both efficient and certain: thanks to rigorous a posteriori error bounds, we may retain only the minimal number of modes necessary to achieve the prescribed accuracy in the output of interest. The technique is particularly appropriate for applications such as design, optimization, and control, in which repeated and rapid evaluation of the output is required. In this paper three versions of this method are presented: (i) for coercive equilibrium problems, (ii) for symmetric eigenvalue problems, and (iii) for non-coercive equilibrium problems.

Type: Proceedings paper
Title: An overview of blackbox reduced-basis output bound methods for elliptic partial differential equations
Event: 16th IMACS World Congress
Location: Lausanne, Switzerland
Dates: 21 August 2000 - 25 August 2000
Open access status: An open access version is available from UCL Discovery
Publisher version: http://at.yorku.ca/cgi-bin/calendar/d/faaf78
Language: English
Additional information: This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: output bounds, reduced-basis techniques, a posteriori error estimation, partial differential equations. AMS subject
UCL classification: UCL
UCL > Provost and Vice Provost Offices
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/10062892
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