Domain decomposition parallel algorithms for one-and two-dimensional diffusion equations are studied by using multi-step evaluation revisions for interface points with fractional temporal index.Stability conditions are loose.In the algorithm,schemes with fractional step and large spacing discretization are used to evaluate interface points.The algorithms have same accuracy as full implicit method,while their stability bounds are released by q,the number of fractional step evaluations on interfaces between two neighboring temporal steps,times compared with existing algorithms.Convergence is proven rigorously with discrete maximum principle.Numerical experiments on parallel computers confirnl theoretical conclusions.They demonstrate looser stability conditions,good accuracy and parallel expansibility of the algorithms.

Two kinds of Stencil elimination schemes with preserved symmetry are presented.Correlative symmetric positive definite difference equations are obtained.Condition number of coefficient matrix decreases over 7/9 folding ratio than that of five point difference Jacobi's.Their eigenvalues have a good clustered spectrum.Theoretic analysis and numerical experiments show that they are better than un-symmetric ones,and are more useful.

A reordering method,named alternate hyperplane ordering,is proposed to solve linear systems from two-dimension three-temperature nonlinear energy equations.Numerical experiments are performed with Krylov subspace iterative associated ILU(k) preconditioning.It is showed that with nearly same preconditioning cost,the proposed ordering method is better than red-black ordering and hyperplane ordering etc.

We present a variant restricted Additive Schwarz preconditioner and apply Partial-Newton-Krylov-Schwarz algorithm to solve nonlinear algebraic equations of two-dimensional three-temperature systems. Iteration and CPU time for convergence are decreased. Numerical results show efficiency of the method.

On the basis of pseudo elimination (PE) approach,the algorithm of the block two stage multisplitting (TSM) interative method for linear systems of the form Ax=f is proposed,when A is block tridiagonal matrix.The resulting multisplitting pseudo elimination(MPPE) method has been tested on a Challeng-L and power PC Cluster computer.Numerical examples are also given.

Algorithms of the block multisplitting and preconditioned Krylov iterative Method for linear systems of the form Ax=f are proposed,where A is block tridiagonal matrix. The convergence of these iterative methods is analysed,when A is an M matrix or H matrix.The resulting MPPE method and preconditioned AKrylov method have been tested on a Challenge L computer.Numerical examples indicates that the new method is very efficient,since the parallel computation can be applied.

The algorithms of Vectorizable PE Method for linear systems of the form Ax=f are proposed, when A is block tridiagonal matrix. The convergence of these iterative methods is analysed, when A is an M matrix or H matrix. The resulting VPE method has been tested on YH-1 computer. Numericla examples indicate that the new method is very efficient, since the vectorial computation can be applied.

An algorithm is proposed of the preconditioned generalized conjugate residual method for solving unsymmetric linear systems on a vector multiprocessor, when A is a five, seven or nine-diagonal matrix. The convergence of this iterative method is analysed. In this algorithm the iterations number is vesified to be about the same as for the multiprocessor PGCR algorithms.The resulting preconditioned GCR method has been tested by simulating a parallel-vector computer.Numerical examples indicate that the new algorithm is very efficient, when the vector multiprocessor computation is applied.

The higher ordar parallel Jacobi-Type method for solving system of linear algebraic equations is proposed, the convergence of the method is analysed and the optimum parameters and the corresponding spectral radius of the iterative matrix for the model proplem and the like are given. In the end there are some numerical examples to illustrate the effectiveness of our method.

In this paper the Monte Carlo method in 2D and 3D is used to calculate the damage probability resulted from shrapnel-attack on the target, in addition, an exact analytical formula for 2D uniform distribution is also proposed.

In this paper, a parallel block accelerated overralaxation Jacobi iterative method is proposed; the rate of convergence is analysed when the coefficient matrix A is symmetric positive definite and H-matrix, Numerical examples are given.

In this paper several SIP algorithms are proposed and the choice of their optimal parametens are analyzed in the case where the coefficient matrix of the linear system is an L-matrix with nonvanishing diagonal elements. Numerical results are given to illustrate that the convergence of our algorithms with the optimal parameters is better than that of other algorithms and parameters.