Based on two-dimensional domain decomposition with small overlapping,we provide a method in which local lower and upper triangular incomplete factors are combined into an effective approximation for global incomplete lower and upper triangular factors of coefficient matrix.Parallelization method is applicable to any preconditioner of incomplete type. Parallel performance metric of two-dimensional parallel preconditioner is compared to that of one-dimensional ones.Experiments show that it is more efficient than additive Schwarz technique and two-dimensional decomposition is better than corresponding one-dimensional decomposition as more processors are used for parallel computation.

Based on one-dimensional domain decomposition with small overlapping, we approximate local lower and upper triangular incomplete factors and combine these factors into an effective approximation for global incomplete factorization preconditioner of coefficient matrix. Two implementations are considered. One is based on exchange of total boundary values of overlapped domain. The other is based on carefully arranged computation process to reduce communication of whole overlapped domain in one line of grid points. The parallelization method can be used to any incomplete factorization preconditioner. Experiments show that it is more efficient than widely-used additive Schwarz technique.

A parallel algorithm (PAA algorithm) is presented for the solution of diagonally dominant periodic tridiagonal linear systems. Its computation complexity is O(8n) and its communication complexity is O(1). But now the computation and communication complexity of the best parallel algorithm are O(17n) and O (log P) respectively. The PAA algorithm is implemented on the SGI Indy workstation cluster. The results show that the speed up has been improved linearly and the paralleling efficiency reaches to 90%.

By using the formalism ofsecond quantization and irreducible tensor,quasispin angular momentum scalaroperator Z(K),where K=2,…,2j,is constructed from 4 creation-annihilation operators.Theeigenvalues of Z(K) have special ability for classification of coupled states,by angular momentum J and quasispin Q the complete classification can be done only for j≤7/2,but by eigenvalues of Z(K)the complete classification have be donefor j≤15/2.The methods for calculating the eigenvalues of Z(K)are discussed,and the complete classifications for j≤15/2 are presented.

Four different types of serial multigrid preconditioned conjugate gradient algorithms are applied to treat interface problems, and their numerical convergence rates are also compared with respect to interface types, interface degree and stepsize. Schwarz parallelism is used for algorithms, and discussion concerns the convergence rates with respect to the number of subdomains, and the benefits owing to Schwarz parallelism. Detailed performence results are also given.

Four numerical methods for calculating coefficients of fractional parentage(CFP) of nucleons are compared,and the results show that the method of complete space by neutron-proton couplied is much better than that of over complete space,the method of factorization by group chains is much better than that of non factorization,and there are great differences of calculating amonut between different methods.

Visualization In Scientific Computing (VISC) is a rapidly developing application of computer graphics. This paper introduces a Visualization System In Quantum Mechanics-VISQUM, and discusses some methods and techniques used in this system.

A bisection method is presented for solving the eigenvalue problem of symmetric band matrices.This method is especially suitable for the case where only a few eigenpairs are needed. Further more,a modified strategy is also presented.The main idea is that firstly using the bisection for some steps to obtain an approximate eigenvalue,then Rayleigh Quotient Iteration is applied to extract the eigenvalue to a predifined accuracy.