论文标题
通过有限元方法在无限域上求解非线性klein-gordon方程
Solving nonlinear Klein-Gordon equations on unbounded domains via the Finite Element Method
论文作者
论文摘要
大量的标量调节理论具有筛选机制，该机制会动态抑制太阳系和局部实验室实验中的第五力。从技术上讲，在标量场方程级别上，这通常转化为非线性，这些非线性强烈限制了分析方法的范围。本文介绍了基于有限元方法（FEM）和牛顿方法的$ trestoscope $ $ - $ $ $ $ $ $ $ - $ $ - $ $ - $ - $ $ - $ - $ - $ - $ - $ - $ - $ - $ $ - $ $ - 用于求解klein-gordon的方程式，这些方程式尤其是在symmetron或chameleon模型中出现的。关于后者，标量场行为通常仅是无限远离其来源的无限远的。因此，我们研究了有限记忆计算机上的渐近边界条件的现有和新的基于FEM的技术，该计算机的收敛性评估。最后，通过研究地球轨道上的Chameleon第五力量的研究，展示了$ themtoscope $。
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.
