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

量子色动力学(QCD)是夸克和胶子共同作用的量子理论。它应该阐明从低能到高能的强力的物理学原理。已知的直接攻击是格子方法。这个理论被称为格子QCD(LQCD)。一个重要的例子是用Neuberger费米子模拟格子QCD。这项研究中最重要的问题是寻找大型线性方程组的近似解。从并行计算的角度来看，迭代Krylov求解器在近似求解这样的大型线性方程组时是很受欢迎的。除了工具包的设计外，我们还给出了我们的方法来组成Krylov空间生成及其预条件的不同组合，以及每一步对残差施加的正交性条件，从而产生了不同的算法。通常，Krylov子空间方法必须与预条件一起使用，由于其并行的性质，使用近似逆已成为隐式预条件的一种很好的替代。主要应用于具有给定稀疏模式的矩阵的子空间，该稀疏模式通过增加每列中的非零项的集合来迭代构造。我们发展了三种并行近似逆预条件子：(I)牛顿型，(Ii)极小残值型，(Iii)Sherman-Morrison型。上述稀疏预条件子的有效性也被其它偏微分方程组的数值实验所证明。我们目前的工作将继续掩盖更一般的数值问题及其分析。

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.