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.Comment: Correction of typography in Table I (p.7