Prud'homme, C;
Rovas, DV;
Veroy, K;
Machiels, L;
Maday, Y;
Patera, AT;
Turinici, G;
(2002)
Reduced-basis Output Bound Methods for Parametrised Partial Differential Equations.
In:
Proceedings of Proceedings of the Singapore MIT Alliance Symposium 2002.
Massachusetts Institute of Technology: Saarbrücken, Germany.
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Abstract
An efficient and reliable method for the prediction of outputs of interest of partial differential equations with affine parameter dependence is presented. To achieve efficiency we employ the reduced-basis method: a weighted residual Galerkin-type method, where the solution is projected onto low-dimensional spaces with certain problem-specific approximation properties. Reliability is obtained by a posteriori error estimation methods - relaxations of the standard error-residual equation that provide inexpensive but sharp and rigorous bounds for the error in outputs of interest. Special affine parameter dependence of the differential operator is exploited to develop a two-stage off-line/on-line blackbox computational procedure. In the on-line stage, for every new parameter value, we calculate the output of interest and an associated error bound. 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 thus ideally suited for the repeated and rapid evaluations required in the context of parameter estimation, design, optimization, and real-time control. The theory and corroborating numerical results are presented for: symmetric coercive problems (e.g. problems in conduction heat transfer), parabolic problems (e.g. unsteady heat transfer), noncoercive problems (e.g. the reduced-wave, or Helmholtz, equation), the Stokes problem (e.g flow of highly viscous fluids), and certain nonlinear equations (e.g. eigenvalue problems).
| Type: | Proceedings paper |
|---|---|
| Title: | Reduced-basis Output Bound Methods for Parametrised Partial Differential Equations |
| Event: | Singapore MIT Alliance Symposium 2002 |
| Location: | Saarbrücken, Germany |
| Open access status: | An open access version is available from UCL Discovery |
| Publisher version: | https://dspace.mit.edu/handle/1721.1/16956 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Mechanical Engineering. |
| 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/10062917 |
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