标题： GWsim：一个模拟在势阱中传播的引力波的代码 显示英文标题

标题： GWsim: a code to simulate gravitational waves propagating in a potential well

摘要： 我们提出了一种代码，用于在时域中模拟引力波在势阱中的传播。 我们的代码基于公开可用的代码{\it deal.ii}，使用有限元方法（FEM）。 我们使用点源单色球面波来测试我们的代码。 我们不仅检查了局部观察者观测到的波形，还检查了波的全局能量守恒。 我们发现数值结果与分析预测非常吻合。 基于我们的代码，我们研究了引力波的前沿在势阱中的传播。 我们发现数值结果与通过追踪零测地线得到的结果非常吻合。 基于我们的模拟，我们还测试了薄透镜模型在预测波前位置方面的准确性。 我们发现Shapiro时间延迟的分析公式仅在远离势阱中心的区域是准确的。 然而，在光轴附近，分析公式与模拟结果有显著差异。 除了这些结果外，我们发现与几何光学中的常规图像不同，由于波效应，引力波不能被散射体遮挡。 引力波的信号可以绕过散射体，并沿光轴传播直到到达远处的观察者，这是该系统中的一个重要观测结果。 显示英文摘要

摘要： We present a code to simulate the propagation of GWs in a potential well in the time domain. Our code uses the finite element method (FEM) based on the publicly available code {\it deal.ii}. We test our code using a point source monochromatic spherical wave. We examine not only the waveform observed by a local observer but also the global energy conservation of the waves. We find that our numerical results agree with the analytical predictions very well. Based on our code, we study the propagation of the leading wavefront of GWs in a potential well. We find that our numerical results agree with the results obtained from tracing null geodesics very well. Based on our simulations, we also test the accuracy of the thin-lens model in predicting the positions of the wavefront. We find that the analytical formula of the Shapiro-time delay is only accurate in regimes that are far away from the center of the potential well. However, near the optic axis, the analytical formula shows significant differences from the simulated ones. Besides these results, we find that unlike the conventional images in geometric optics, GWs can not be sheltered by the scatterer due to wave effects. The signals of GWs can circle around the scatterer and travel along the optic axis until arrive at a distant observer, which is an important observational consequence in such a system.