Improved Successive Constraint Method Based A Posteriori Error Estimate for Reduced Basis Approximation of 2D Maxwells Problem

Yanlai Chen; Jan Sickmann Hesthaven; Yvon Maday; Jerónimo Rodríguez

Improved Successive Constraint Method Based A Posteriori Error Estimate for Reduced Basis Approximation of 2D Maxwells Problem

Yanlai Chen Jan Sickmann Hesthaven Yvon Maday Jerónimo Rodríguez ¹

1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation

Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231

Abstract : In a posteriori error analysis of reduced basis approximations to affinely parametrized partial differential equations, the construction of lower bounds for the coercivity and inf-sup stability constants is essential. In [7], the authors presented an efficient method, compatible with an off-line/on-line strategy, where the on-line computation is reduced to minimizing a linear functional under a few linear constraints. These constraints depend on nested sets of parameters obtained iteratively using a greedy algorithm. We improve here this method so that it becomes more efficient due to a nice property, namely, that the computed lower bound is monotonically increasing with respect to the size of the nested sets. This improved evaluation of the inf-sup constant is then used to consider a reduced basis approximation of a parameter dependent electromagnetic cavity problem both for the greedy construction of the elements of the basis and the subsequent validation of the reduced basis approximation. The problem we consider has resonance features for some choices of the parameters that are well captured by the methodology.

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https://hal-ensta-paris.archives-ouvertes.fr//hal-00976057
Contributor : Aurélien Arnoux <>
Submitted on : Wednesday, April 9, 2014 - 3:33:04 PM
Last modification on : Wednesday, July 3, 2019 - 10:48:03 AM

Improved Successive Constraint Method Based A Posteriori Error Estimate for Reduced Basis Approximation of 2D Maxwells Problem

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Improved Successive Constraint Method Based A Posteriori Error Estimate for Reduced Basis Approximation of 2D Maxwells Problem

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Improved Successive Constraint Method Based A Posteriori Error Estimate for Reduced Basis Approximation of 2D Maxwells Problem