An optimization-based method for sign-changing ...
Type de document :
Article dans une revue scientifique: Article original
DOI :
Titre :
An optimization-based method for sign-changing elliptic PDEs
Auteur(s) :
Abdulle, Assyr [Auteur]
Ecole Polytechnique Fédérale de Lausanne [EPFL]
Lemaire, Simon [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]
Ecole Polytechnique Fédérale de Lausanne [EPFL]
Ecole Polytechnique Fédérale de Lausanne [EPFL]
Lemaire, Simon [Auteur]

Reliable numerical approximations of dissipative systems [RAPSODI]
Ecole Polytechnique Fédérale de Lausanne [EPFL]
Titre de la revue :
ESAIM: Mathematical Modelling and Numerical Analysis
Pagination :
2187-2223
Éditeur :
Société de Mathématiques Appliquées et Industrielles (SMAI) / EDP
Date de publication :
2024
ISSN :
2822-7840
Mot(s)-clé(s) en anglais :
Sign-shifting PDEs
Metamaterials
Finite elements
Domain decomposition
Optimization
Metamaterials
Finite elements
Domain decomposition
Optimization
Discipline(s) HAL :
Mathématiques [math]/Analyse numérique [math.NA]
Résumé en anglais : [en]
We study the numerical approximation of sign-shifting problems of elliptic type. We fully analyze and assess the method briefly introduced in [Abdulle, Huber, Lemaire; CRAS, 17]. Our method is based on domain decomposition ...
Lire la suite >We study the numerical approximation of sign-shifting problems of elliptic type. We fully analyze and assess the method briefly introduced in [Abdulle, Huber, Lemaire; CRAS, 17]. Our method is based on domain decomposition and optimization. Upon an extra integrability assumption on the exact normal flux trace along the sign-changing interface, our method is proved to be convergent as soon as, for a given loading, the PDE admits a unique solution of finite energy. Departing from the $\texttt{T}$-coercivity approach, which relies on the use of geometrically fitted mesh families, our method works for arbitrary (interface-compliant) mesh sequences. Moreover, it is shown convergent for a class of problems for which $\texttt{T}$-coercivity is not applicable. A comprehensive set of test-cases complements our analysis.Lire moins >
Lire la suite >We study the numerical approximation of sign-shifting problems of elliptic type. We fully analyze and assess the method briefly introduced in [Abdulle, Huber, Lemaire; CRAS, 17]. Our method is based on domain decomposition and optimization. Upon an extra integrability assumption on the exact normal flux trace along the sign-changing interface, our method is proved to be convergent as soon as, for a given loading, the PDE admits a unique solution of finite energy. Departing from the $\texttt{T}$-coercivity approach, which relies on the use of geometrically fitted mesh families, our method works for arbitrary (interface-compliant) mesh sequences. Moreover, it is shown convergent for a class of problems for which $\texttt{T}$-coercivity is not applicable. A comprehensive set of test-cases complements our analysis.Lire moins >
Langue :
Anglais
Comité de lecture :
Oui
Audience :
Internationale
Vulgarisation :
Non
Collections :
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