Model reduction of semiaffinely parameterized partial differential equations by two-level affine approximation

We propose an improvement to the reduced basis method for parametric partial differential equations. An assumption of affine parameterization leads to an efficient offline-online decomposition when the problem is solved for many different parametric configurations. We consider an advection-diffusion problem, where the diffusive term is nonaffinely parameterized and treated with a two-level affine approximation given by the empirical interpolation method. The offline stage and a posteriori error estimation is performed using the coarse-level approximation, while the fine-level approximation is used to perform a correction iteration that reduces the actual error of the reduced basis approximation while keeping the same certified error bounds.


Published in:
Comptes rendus des séances de l'Académie des Sciences. Série A, Sciences mathématiques**, 349, 61-66
Year:
2011
ISSN:
0249-6291
Keywords:
Note:
MATHICSE report 20.2010
Laboratories:




 Record created 2010-11-17, last modified 2018-03-17

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