Numerical Astronomy with Parallel Computers

在天文系统中，典型的是在自引力作用下密度对比的出现。在对这类系统的演化进行数值模拟时，有两个主要的困难。首先，我们必须计算所有粒子对之间的引力相互作用。其次，密度对比带来的局部时间尺度差异很大。本研究的目的是通过并行计算来解决这些困难，并为未来的天文模拟提供一种策略。本文主要分析了球状星团的引力多体问题和动态演化问题。比较了不同类型的算法，如需要N^2步的重力直接计算和允许NlogN步的树形算法，以及不同类型的向量机和并行计算机，如PAX和Connection Machine。研究发现，复杂算法的并行化能力不足，而简单的直接算法需要太多的计算步骤。因此，我考虑了构建专用计算机的可能性，并发现一个简单的架构可以解决上面提到的两个困难，同时允许广泛的应用。它是一种在流水线中实现独立时间步长的Aarseth代码的硬件实现。它计算一个粒子的运动，在其他粒子中首先到达下一个时间步。在它的前半部分，其他粒子的坐标是从它们自己的独立时间推断出来的。在它的后半部分，计算作用在更新粒子上的引力。不同粒子的坐标流经管道，执行大约50个浮点计算。设置多个管道并行也很容易，因为它们之间的相互作用只在收集来自不同管道的引力的最后阶段出现。

In astronomical systems typical is the appearance of density contrast under self-gravitation. In numerical simulation for evolution of such systems there are two major difficulties. Firstly, we have to calculate gravitational interactions between all pairs of particles. Secondly, the density contrast brings about gratly different local time scales. The aims of the present research have been to resolve these difficulties by means of parallel computations and to extend a strategy for future astronomical simulations. Analyzed have been such problems mainly for gravitational many body problems and dynamical evolution of globular clusters. Compared have been different types of algorithms such as direct calculation of gravity requiring N^2 steps and tree algorithms allowing NlogN steps, and different types of vector machines and parallel computers such as PAX and Connection Machine. It has been found that the parallelization could only be performed insufficiently for the sophisticated algorithms while the simple direct algorithm requires too much computational steps.Thus, I have considered a possibility to construct special purpose computers and found that a simple architecture is possible to resolve the two difficulties mentioned above yet to allow a wide range of applications. It is a hardware realizing Aarseth code of independent time steps in a pipeline. It calculates the motion of one particle to update that reaches its next time step in the first place among others. In its earlier half the coordinates of the other particles are extrapolated from Their own independent times. In its later half the gravitational force acting on the updating particle is calculated. The coordinates of different particles flow through the pipeline performing about 50 floating point calculations. It is also easy to set many pipelines in parallel because the interaction between them appears only in the final stage of gathering gravitational forces contributing from different pipelines.