ADM方程数值模拟的谱方法
A spectral approach to numerical simulations of the ADM equations
摘要：
为了模拟引力场的动力学过程，我们根据Arnowitt-Deser-Misner（ADM）形式对爱因斯坦方程进行了数值研究.我们考虑了原始的$3+1$分解的ADM方程，在真空条件下，在简化的几何形状。数字代码基于频谱方法，利用滤波（去混叠）技术。该算法已经稳定通过自适应时间细化的基础上，检查自我一致的解决方案的规律性的程序。我们的数值模型的准确性已通过一系列标准测试进行了验证。最后，我们还提出了一种新的初始数据，可用于测试数字代码。
英文摘要：
We present a numerical study of the Einstein equations, according to the Arnowitt-Deser-Misner (ADM) formalism, in order to simulate the dynamics of gravitational fields. We took in consideration the original $3+1$ decomposition of the ADM equations, in vacuum conditions, in simplified geometries. The numerical code is based on spectral methods, making use of filtering (de-aliasing) techniques. The algorithm has been stabilized via an adaptive time-refinement, based on a procedure that checks self-consistently the regularity of the solutions. The accuracy of our numerical model has been validated through a series of standard tests. Finally, we present also a new kind of initial data that can be used for testing numerical codes.
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