Solving nonlinear Klein-Gordon equations on unbounded domains via the finite element method - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Physical Review D Année : 2022

Solving nonlinear Klein-Gordon equations on unbounded domains via the finite element method

Résolution d'équations de Klein-Gordon non-linéaires sur des domaines non-bornés via la méthode des éléments finis

Résumé

A large class of scalar-tensor theories of gravity exhibit a screening mechanism that dynamically suppresses fifth forces in the Solar system and local laboratory experiments. Technically, at the scalar field equation level, this usually translates into nonlinearities which strongly limit the scope of analytical approaches. This article presents femtoscope-a Python numerical tool based on the Finite Element Method (FEM) and Newton method for solving Klein-Gordon-like equations that arise in particular in the symmetron or chameleon models. Regarding the latter, the scalar field behavior is generally only known infinitely far away from the its sources. We thus investigate existing and new FEM-based techniques for dealing with asymptotic boundary conditions on finite-memory computers, whose convergence are assessed. Finally, femtoscope is showcased with a study of the chameleon fifth-force in Earth orbit.
Fichier principal
Vignette du fichier
accepted-version.pdf (6.79 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03795054 , version 1 (03-10-2022)
hal-03795054 , version 2 (20-01-2023)

Identifiants

Citer

Hugo Lévy, Joël Bergé, Jean-Philippe Uzan. Solving nonlinear Klein-Gordon equations on unbounded domains via the finite element method. Physical Review D, 2022, 106 (12), ⟨10.1103/PhysRevD.106.124021⟩. ⟨hal-03795054v2⟩
36 Consultations
35 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More