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

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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.