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Improved successive constraint method based a posteriori error estimate for reduced basis approximation of 2D Maxwell's problem

Yanlai Chen, Jan S. Hesthaven, Yvon Maday, Jerónimo Rodríguez (2009)

ESAIM: Mathematical Modelling and Numerical Analysis


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 [Huynh et al., C. R. Acad. Sci. Paris Ser. I Math.345 (2007) 473–478], 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...

Integral Equations VIA Saddle Point Problem for 2D Electromagnetic Problems

Nathalie Bartoli, Francis Collino (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

A new system of integral equations for the exterior 2D time harmonic scattering problem is investigated. This system was first proposed by B. Després in [11]. Two new derivations of this system are given: one from elementary manipulations of classical equations, the other based on a minimization of a quadratic functional. Numerical issues are addressed to investigate the potential of the method.

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