A toy model for testing finite element methods to simulate extreme-mass-ratio binary systems
A toy model for testing finite element methods to simulate extreme-mass-ratio binary systems
复制标题
用于测试模拟极端质量比二元系统的有限元方法的玩具模型
DOI：
--
复制
发表时间：
2005
期刊：
影响因子：
--
通讯作者：
Jinchao Xu
中科院分区：
文献类型：
--
作者：
C. Sopuerta;Pengtao Sun;P. Laguna;Jinchao Xu
极端质量比双星系统，即涉及绕大质量黑洞运行的恒星质量物体的双星，被认为是天基干涉仪丽莎探测的引力辐射的主要来源。这些二元系统的数值模拟极具挑战性，因为涉及的尺度扩展到几个数量级。人们需要处理与大质量黑洞大小相当的大波长尺度，同时要解决小伴星附近的尺度，在那里辐射反应效应起着至关重要的作用。自适应有限元方法，其中定量控制的错误是自动实现的有限元网格自适应后验误差估计的基础上，是一个自然的选择，具有很大的潜力，实现高水平的自适应性，这些模拟所需的。为了证明这一点，我们提出了一个玩具模型的模拟结果，包括一个点状源的标量引力场的作用下绕黑洞。
Extreme-mass-ratio binary systems, binaries involving stellar mass objects orbiting massive black holes, are considered to be a primary source of gravitational radiation to be detected by the space-based interferometer LISA. The numerical modelling of these binary systems is extremely challenging because the scales involved expand over several orders of magnitude. One needs to handle large wavelength scales comparable to the size of the massive black hole and, at the same time, to resolve the scales in the vicinity of the small companion where radiation reaction effects play a crucial role. Adaptive finite element methods, in which quantitative control of errors is achieved automatically by finite element mesh adaptivity based on a posteriori error estimation, are a natural choice that has great potential for achieving the high level of adaptivity required in these simulations. To demonstrate this, we present the results of simulations of a toy model, consisting of a point-like source orbiting a black hole under the action of a scalar gravitational field.