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Unstructured Multi-Grid method and the efficient implementation technique on parallel machines

非结构化多重网格方法及并行机高效实现技术

基本信息

批准号：
15607005
负责人：
OYANAGI Yoshio
金额：
$ 2.24万
依托单位：
University of Tokyo
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2005
项目状态：
已结题

项目摘要

Efficient preconditioning for Conjugate Gradient method requires parallelization and good acceleration of convergence. These two things are often incompatible. Thus, the authors proposed the Multi-Grid preconditioning, which satisfies both of two things, and have demonstrated the efficiency of the method.In this study, we considered the problems with unstructured grids and with a big anisotropy. SA-AMG method, which is one of the multi-grid methods, calculates the smaller matrix and reaches the convergence efficiently utilizing that smaller matrix. But the SA-AMG method's efficiency deteriorates for anisotropic problems. The authors have shown that the smaller matrix creation method based on domain border information enables the method efficient convergence.We also studied the vectorization of the SA-AMG method for the implementation technique. Three matrix multiplications occupy the most calculation cost. For vectorization of this part, we tested various combinations of sparse matrix … More data structures and demonstrated the method based on the JDS and the CRS data structures is the most efficient for 3-Dimentional elastic problems. For another related study of the implementation technique, the authors created the re-distribution and re-ordering library for distributed sparse matrix. This library offers the frame work of the dynamic re-distribution and re-ordering, and enables those things easily.For other study of basic parallel implementation technique, the authors have studied the redistribution scheduling problem for finite sized multi-master divisible load problem. By identification of some parameters the authors showed that the simulation duplicates the behavior of the real system. We have also studied data distribution problem of the parallel molecular dynamics, and researched the best data distribution method in the case that the communication band-width and latency between computer nodes are not uniform. It is a challenge for the future to apply these basic techniques for parallel implementation of multi-grid method on various computer platforms. Less

共轭梯度法的有效预处理需要并行化和良好的收敛加速。这两件事往往是不相容的。因此，作者提出了多重网格预处理方法，它同时满足两个条件，并证明了该方法的有效性。SA-AMG方法是多重网格方法中的一种，它计算较小的矩阵，并利用该较小的矩阵有效地达到收敛。但是SA-AMG方法对于各向异性问题的效率变差。作者证明了基于域边界信息的小矩阵生成方法使该方法有效收敛，并研究了SA-AMG方法的矢量化实现技术。三个矩阵乘法占用了最多的计算成本。对于这部分的矢量化，我们测试了稀疏矩阵的各种组合 ...更多信息数据结构，并证明了基于JDS和CRS数据结构的方法是求解三维弹性问题的最有效方法。在相关实现技术的研究中，作者建立了分布式稀疏矩阵重分布重排序库。该库提供了动态重分配和重排序的框架，并使这些事情变得容易。在基本并行实现技术的其他研究中，作者研究了有限大小的多主可分负载问题的重分配调度问题。通过对一些参数的辨识，作者表明，模拟再现了真实的系统的行为。本文还研究了并行分子动力学的数据分配问题，研究了在计算机节点间通信带宽和延迟不均匀的情况下的最佳数据分配方法。如何将这些基本技术应用于多重网格方法在不同计算机平台上的并行实现是未来的一个挑战。少