标题： 利用有限元方法模拟低频引力波在致密天体上的散射 显示英文标题

标题： Simulating the scattering of low-frequency Gravitational Waves by compact objects using the finite element method

摘要： 我们利用基于公开代码{\it deal.ii}的有限元法（FEM）数值模拟，研究了引力波（GWs）的波效应。 我们通过点源单色球面波稳健地测试了我们的代码。 我们不仅检查了局部观察者观测到的波形，还考察了波的全局能量守恒情况。 我们发现数值结果与解析预测非常吻合。 基于我们的代码，我们研究了紧致天体对引力波的散射。 使用单色波作为输入源，我们发现如果引力波的波长远大于紧致天体的史瓦西半径，则对于远离散射体的观测者而言，由于强衍射效应，总散射引力波的振幅几乎不会显著变化。 这一发现与文献中的结果一致。 然而，我们也发现，在靠近散射体的地方，不仅散射波的振幅非常大，且与入射波相当，而且由于散射波和入射波之间的干涉作用，引力波的相位发生了显著变化。 由于引力波相位的演化在从噪声背景中提取引力波信号的匹配滤波技术中起着关键作用，我们的发现表明，未来低频引力波实验的数据分析中应考虑波效应，尤其是在引力波被附近紧致天体散射的情况下。 显示英文摘要

摘要： We investigate the wave effects of gravitational waves (GWs) using numerical simulations with the finite element method (FEM) based on the publicly available code {\it deal.ii}. We robustly 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 very well with the analytical predictions. Based on our code, we study the scattering of GWs by compact objects. Using monochromatic waves as the input source, we find that if the wavelength of GWs is much larger than the Schwarzschild radius of the compact object, the amplitude of the total scattered GWs does not change appreciably due to the strong diffraction effect, for an observer far away from the scatterer. This finding is consistent with the results reported in the literature. However, we also find that, near the scatterer, not only the amplitude of the scattered waves is very large, comparable to that of the incident waves, but also the phase of the GWs changes significantly due to the interference between the scattered and incident waves. As the evolution of the phase of GWs plays a crucial role in the matched filtering technique in extracting GW signals from the noisy background, our findings suggest that wave effects should be taken into account in the data analysis in the future low-frequency GW experiments, if GWs are scattered by nearby compact objects in our local environment.