权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Constraction of the lattice gauge computation tools for large scale cluster computars

大规模集群计算机格子规范计算工具的构建

基本信息

批准号：
15540136
负责人：
NODERA Takashi
金额：
$ 2.18万
依托单位：
Keio University
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

Quantum Chromo dynamics (QCD) is the quantum theory of working together with quarks and gluons. It should make clear the physics of strong force from low to high energies. The direct attack it is known to be the lattice approach. This theory is called to be Lattice QCD (LQCD).One important example is simulations in Lattice QCD with Neuberger fermions. The most important problem in this research is to find an approximate solution to the large linear systems of equations. From parallel computational point of view, iterative Krylov solvers are admired for approximately solving such the large linear systems of equations. In addition to the design of the toolkit, we have presented our approach to make up the different combinations of Krylov space generation and its preconditioning along with the orthogonality condition imposed on the residual at each step give rise to the different algorithms.Generally, Krylov subspace methods have to be used with preconditiong, The use of approximate inverses have become a good alternative to implicit preconditioners due to their parallel nature. The main application is developed for the subspace of matrices with a given sparsity pattern which constructed iteratively by augmenting the set of non-zero entries in each column. We are developed three types of parallel approximate inverse preconditioner as follows,(i)Newton type, (ii)Minimal residual type, (iii)Sherman-Morrison typeThe effectiveness of the above sparse preconditioners was also shown with some numerical experiments of other PDE problems.Our present work will be continued to cover up more general numerical problems and their analysis.

量子染色体动力学（QCD）是研究夸克和胶子共同作用的量子理论。它应该使从低能量到高能量的强力物理学变得清晰。已知的直接攻击是格方法。这种理论被称为格点QCD（LQCD），其中一个重要的例子是用Neuberger费米子模拟格点QCD。在这项研究中最重要的问题是找到一个大型线性方程组的近似解。从并行计算的角度来看，迭代Krylov解算器是推崇近似求解这样的大型线性方程组。除了工具包的设计之外，我们还提出了我们的方法来组成Krylov空间生成和预处理的不同组合，沿着在每一步对残差施加的正交条件，从而产生不同的算法。由于近似逆的并行性质，近似逆的使用已经成为隐式预条件子的一个很好的替代方案。主要的应用程序是开发的子空间的矩阵与一个给定的稀疏模式，构造迭代增加的非零元素在每列中的集合。本文提出了三种并行近似逆预条件子：（i）Newton型，（ii）最小剩余型，（iii）Sherman-Morrison型，这些稀疏预条件子的有效性也通过其它偏微分方程问题的数值实验得到了证明。