An optimization-based method for sign-changing elliptic PDEs

Abdulle, Assyr; Lemaire, Simon

Document type :

Pré-publication ou Document de travail

Title :

An optimization-based method for sign-changing elliptic PDEs

Author(s) :

Abdulle, Assyr [Auteur]
Ecole Polytechnique Fédérale de Lausanne [EPFL]
Lemaire, Simon [Auteur]

Ecole Polytechnique Fédérale de Lausanne [EPFL]
Reliable numerical approximations of dissipative systems [RAPSODI]

Publication date :

2023-06-25

English keyword(s) :

Sign-shifting PDEs
Metamaterials
Finite elements
Domain decomposition
Optimization

HAL domain(s) :

Mathématiques [math]/Analyse numérique [math.NA]

English abstract : [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, 2017]. Our method, which is based on domain ...
Show more >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, 2017]. Our method, which is based on domain decomposition and optimization, is proved to be convergent as soon as, for a given loading, the continuous problem 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) meshes and anisotropic coefficients. 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.Show less >

Language :

Anglais

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

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