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Three dimensional numerical relativity using parallel super computers

使用并行超级计算机的三维数值相对论

基本信息

批准号：
10640227
负责人：
OOHARA Ken-ichi
金额：
$ 1.47万
依托单位：
NIIGATA UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 2000
项目状态：
已结题

项目摘要

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.

我开发了研究合并中子星双星和引力波辐射的数值模拟代码，并获得了一个稳定的、高精度的跟踪合并中子星双星演化的代码。代码的基本结构包括：在坐标条件上，空间坐标采用拟最小失真条件，时间坐标采用最大切片条件。我最初采用保形切片作为时间坐标，但在延时函数的演化过程中遇到了不稳定模式。然后我用最大切片代替。在每个时间步长，需要求解6个椭圆型偏微分方程来求解圈函数、位移矢量和保形因子。这些问题的求解采用完全可向量化和并行化的预条件共轭梯度法，但为了实现高速计算，必须对程序进行高度调整，以适应某种超级计算机。采用带TVD的van Leer格式求解广义相对论流体力学方程，采用CIP方法求解度量张量的演化方程。用共形切片法可以简单地从度量摄动中提取引力波，但需要用极大切片法提取量规不变引力波。虽然它还没有实现，我发现一个简单的度量扰动给出了引力波的一个很好的估计，比较两种切片条件的结果。为了得到中子星与引力辐射合并的最终结果，需要更多的计算机能力，但该代码具有可扩展性，很快将在日本国立天文台和/或高能加速器研究机构的新型超级计算机上使用该代码进行中子星合并的研究。