论文标题
用于重力场数值模拟的光谱法算法
A spectral method algorithm for numerical simulations of gravitational fields
论文作者
论文摘要
提出了基于时空的3+1叶的爱因斯坦场方程的数值研究。在两种不同的形式主义中，已经采用了一种伪谱技术进行真空模拟，即Arnowitt-Deser-Misner（ADM）和保形Baumgarte-Shapiro-Shapiro-Shibata-Nakamura（BSSN）方法。数值代码基于傅立叶分解，并伴随着不同的过滤技术。已经研究了交易的作用以及过滤器类型的影响。这些算法已经通过一种新的程序来稳定，该过程可以自愿控制解决方案的规律性。该模型的精度已通过标准测试床进行了验证，表明过滤后的伪谱技术是最准确的方法之一。最后，已经提出了通过黑洞动力学和基于抑制虚假边界问题的过度散布的新策略强调该过程的。该模型代表了一个有效的研究工具，特别适合在重力动力学中检查小规模非线性现象。
A numerical study of the Einstein field equations, based on the 3+1 foliation of the spacetime, is presented. A pseudo-spectral technique has been employed for simulations in vacuum, within two different formalisms, namely the Arnowitt-Deser-Misner (ADM) and the conformal Baumgarte-Shapiro-Shibata-Nakamura (BSSN) approach. The numerical code is based on the Fourier decomposition, accompanied by different filtering techniques. The role of the dealiasing, as well as the influence of the filter type, has been investigated. The algorithms have been stabilized via a novel procedure that controls self-consistently the regularity of the solutions. The accuracy of the model has been validated through standard testbeds, revealing that the filtered pseudo-spectral technique is among the most accurate approaches. Finally, the procedure has been stressed via black hole dynamics and a new strategy, based on hyperviscous dissipation that suppresses spurious boundary problems, has been proposed. The model represents a valid tool of investigation, particularly suitable for the inspection of small scale nonlinear phenomena in gravitational dynamics.
