Within the landscape of modified theories of gravity, progress in understanding the behaviour of, and developing tests for, screening mechanisms has been hindered by the complexity of the field equations involved, which are nonlinear in nature and characterised by a large hierarchy of scales. This is especially true of Vainshtein screening, where the fifth force is suppressed by high-order derivative terms which dominate within a radius much larger than the size of the source, known as the Vainshtein radius. =-1 In this work, we present the numerical code φenics, building on the FEniCS library, to solve the full equations of motion from two theories of interest for screening: a model containing high-order derivative operators in the equation of motion and one characterised by nonlinear self-interactions in two coupled scalar fields. We also include functionalities that allow the computation of higher-order operators of the scalar fields in post-processing, enabling us to check that the profiles we find are consistent solutions within the effective field theory. These two examples illustrate the different challenges experienced when trying to simulate such theories numerically, and we show how these are addressed within this code. The examples in this paper assume spherical symmetry, but the techniques may be straightforwardly generalised to asymmetric configurations. This article therefore also provides a worked example of how the finite element method can be employed to solve the screened equations of motion. φenics is publicly available and can be adapted to solve other theories of screening.

在改良的重力理论领域中，由于涉及的磁场方程的复杂性（本质上是非线性的并且具有较大的尺度层次），阻碍了对筛选机制的理解以及为筛选机制开发测试的进展。对于Vainshtein筛选尤其如此，其中第五力由高阶导数项抑制，这些项在一个比源大小大得多的半径内占主导地位，称为Vainshtein半径。= -1在这项工作中，我们在FEniCS库的基础上给出了φenics的数字代码，用于从两个感兴趣的理论中筛选出完整的运动方程：一个在运动方程中包含高阶导数算子的模型和一个模型。其特征是两个耦合标量场中的非线性自相互作用。我们还包括一些功能，这些功能允许在后处理中计算标量字段的高阶运算符，从而使我们能够检查所找到的轮廓是否是有效字段理论中的一致解。这两个示例说明了尝试对这些理论进行数值模拟时遇到的不同挑战，并且我们展示了如何在代码中解决这些挑战。本文中的示例假定球面对称，但是该技术可以直接推广到不对称配置。因此，本文还提供了一个可行的示例，说明了如何使用有限元方法来求解所筛选的运动方程。φenics是公开可用的，可以进行调整以解决其他筛选理论。