Three dimensional numerical relativity using parallel super computers

我开发了研究并合中子星星双星和引力波辐射的数值模拟程序，得到了一个能高精度跟踪并合中子星星双星演化的稳定程序。代码的基本结构包括：在坐标条件上，空间坐标采用伪最小失真条件，时间坐标采用最大切片条件。起初，我采用共形切片的时间坐标，但面临着不稳定的模式演变的推移函数。然后用最大切片法代替，在每个时间步上求解六个椭圆型偏微分方程，求出重叠函数、位移向量和共形因子。它们使用预处理共轭梯度法求解，该方法可以完全矢量化和并行化，本文用货车Leer格式和TVD方法求解广义相对论流体力学方程组，用CIP方法求解度规张量的演化方程组，计算过程简单，计算量小，计算速度快从度规扰动的共形切片，但规范不变的引力波提取需要与最大切片。虽然它还没有实现，但我发现一个简单的度规扰动在与两种切片条件的结果比较中对引力波给出了很好的估计。为了获得合并中子星星双星和引力辐射的最终结果，需要更多的计算机能力，但该代码具有可扩展性，不久将在日本国家天文台的新超级计算机上使用该代码研究合并中子星星双星，或者高能加速器研究组织

I have developed numerical simulation codes for studying coalescing neutron star binaries and radiation of gravitational waves, and obtained a stabie code which follows the evolution of coalescing neutron star binaries with a high precision. The basic structure of the code includes :As for the coordinate condition, the pseudo-minimal distortion condition for the spatial coordinate and the maximal slicing condition for the time coordinate are used. At first, I adopted the conformal slicing for the time coordinate but was confronted with unstable modes in the evolution of the lapse function. Then I used the maximal slicing instead.Six elliptic partial differential equations mush be solved for the laps function, shift vector and conformal factor at each time step. They are solved using a preconditioned conjugate gradient method that can be fully vectorizable and parallelizable, but in order to achieve a high speed calculation the program must be tuned to high degree for some kind of super computer.The general relativistic hydrodynamics equations are solved using van Leer's scheme with TVD and the evolution equations for the metric tensor are solved using the CIP method.Gravitational waves can be obtained simply from the metric perturbation with the conformal slicing, but gauge-invariant gravitational wave extraction is needed with the maximal slicing. Although it has not yet implemented, I found that a simple metric perturbation gives a good estimate for the gravitational waves in comparison the results with both slicing conditions.To obtain the final results in coalescing neutron star binaries and the gravitational radiation, more computer power is necessary, but the code has scalableness and coalescing neutrons star binaries will be studied soon using the code on new super computer at National Astronomical Observatory Japan and/or the High Energy Accelerator Research Organization.