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 based on the publicly available code 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 centre 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 cannot 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 they arrive at a distant observer, which is an important observational consequence in such a system.

中文翻译：

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gwsim：模拟在势阱中传播的引力波的代码

我们提出了一个代码来模拟 GW 在时域中的势阱中的传播。我们的代码使用基于公开代码 deal.ii 的有限元方法。我们使用点源单色球面波测试我们的代码。我们不仅检查了本地观察者观察到的波形，还检查了波的全局能量守恒。我们发现我们的数值结果与分析预测非常吻合。根据我们的代码，我们研究了 GW 的前导波前在势阱中的传播。我们发现我们的数值结果与通过追踪零测地线获得的结果非常吻合。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，夏皮罗时间延迟的解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，解析公式与模拟公式有显着差异。除了这些结果，我们发现与几何光学中的传统图像不同，由于波浪效应，GWs不能被散射体遮挡。GW 的信号可以围绕散射体旋转并沿光轴传播，直到它们到达远处的观察者，这是此类系统中重要的观测结果。由于波浪效应，GW 不能被散射体遮挡。GW 的信号可以围绕散射体旋转并沿光轴传播，直到它们到达远处的观察者，这是此类系统中重要的观测结果。由于波浪效应，GW 不能被散射体遮挡。GW 的信号可以围绕散射体旋转并沿光轴传播，直到它们到达远处的观察者，这是此类系统中重要的观测结果。