With potential energy surface constructed in 2003, we study stereodynamics of reaction Li+HF→LiF+H using quasiclassical trajectory (QCT) method. Polarization dependent differential cross sections (PDDCSs) and P(θ_r,φ_r) distributions describing k-k'-j' correlation related to collision energies. Vibrational states and rotational states are discussed at 1.15 kcal·mol^-1-5.0 kcal·mol^-1. Furthermore, cross sections are compared with that of other calculations and experiments. It indicates that vibrational and rotational excitations have stronger impacts on PDDCSs and P(θ_r,φ_r) than collision energy. Backscattering polarization of product rotational angular momentum is positive correlated with collision energy. Cross sections agree well with results of other theories and experiments in the range of calculation collision energies.

Parallel computing of direct simulation Monte Carlo (DSMC) based on compute unified device architecture (CUDA) is developed and improved data transmission in multi-GPU parallel computing is devoted to promote parallel efficiency.A two-dimensional Couette flow and lid-driven cavity flow by CPU,single GPU and double GPU parallel computing are simulated,respectively.Precision of results by GPU is consistent with that by CPU and speedup ratio can reach to 10~30 by single GPU acceleration and 40~60 by double GPU acceleration.Speedup efficiency by multi-GPU is approximated to 100%.

We propose a fast random simulation strategy based on differentially weighted MC. The strategy improves computation efficiency significantly, and guarantees enough calculation accuracy, thus coordinates contradiction between computation cost and computation accuracy. The main idea is based on majorant kernel. It is possible to transfer a traditional coagulation kernel to a majorant kernel through splitting and amplifying slightly. The maximum of majornant kernel is obtained by single looping over all simulation particles. The maximum majornant kernel is used to approximate the maximum coagulation kernel in particle population, and is further used to search coagulation particle pairs randomly with acceptance-rejection method. The waiting time (time-step) for a coagulation event is calculated by summing coagulation kerenls of particle pairs involved in acceptance/rejection processes.. Double looping in normal Monte Carlo simulation is avoided and computation efficiency is improved greatly.

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.

We developed a high performance algebraic solver for nonlinear systems discretized from two-dimensional energy equations with three temperatures by a nine point scheme.The main idea is to solve the system by an inexact Newton method and preconditioned Krylov subspace methods in the frame of PNK and JFNK methods.Numerical experiments show the efficiency of the algebraic solvers.It is shown that our PNK method is 6 times faster than the nonlinear block Gauss-Seidel method. The JFNK and PNK methods are also compared.

A high-order accurate algorithm, which consists of WCNS-E-5 for inviscid term, fourth-order accurate scheme for viscous term and corresponding fouth-order boundary scheme, is carried out on the heat transfer distribution on body surface in a hypersonic viscous flow. The effect of grid Reynolds number on heat transfer at stagnation point and the influence of different boundary schemes on heat transfer distribution are investigated. A flow past a blunt cone with high attack angles is simulated numerically. It is shown that WCNS-E-5 is able to permit large spatial scale near the body. The physical phenomena captured by WCNS-E-5 with high-order accuracy are real, clear and high resolving in the whole flowfield. The heat transfer solutions are reliable and accurate.

In a sparse linear system derived from two-dimensional three-temperature energy equations, the diagonal dominan varies greatly from row to row and so is the magnitude of the elements. We provide a new scaling method to improve the diagonal dominance. As ILUT is used to the derived linear system, it reserves the number of elements in each row and several relatively large elements related to the photon are dropped due to the large difference among elements. To improve the equality of the ILUT, we provide a new method named multiple row ILUT (MRILUT), in which multiple rows are computed before dropping. The provided methods are embedded into a preconditioned Krylov subspace method to solve the actual two-dimensional energy equations with three temperatures. The number of iteration at each time step and the total computation time are both greatly reduced.

A new type of hybrid iterative method is presented, which is competent in solving the large scale sparse linear systems derived from the 2-dimensional 3-temperature radiation dynamic energy equations. Numerical results show that the new method is as 4 times fast as the old ones.Especially on the cases the old one doesn't converge, the new method can easily get the solution to the precision required. It can successfully complete the simulation and the final physical parameters of the simulation coincide with the theory.

It presents an effective fill-in technology for the preconditioners of large sparse linear algebraic equations arising from the difference discretizations of high dimensional physical problems, and discusses the relations between fill-in and numerical costs. By using this technology into the practical problems for verification, numerical results obtained are well coincided with the theoretical analyses.

To solve complex systems obtained from 2D nonlinear Schrödinger equation, a method of high-order PCG coupling with BICG has been developed. Meanwhile, the complex systems of order M can be reconstructed as the real systems of order 2M. From the theory of order matrix, the high order approximate LU decompositions are given as the preconditioners to solve the real systems. Numerical results show that the computational efficiency can be nearly doubled by the high-order PCG method comparing with the ICCG method.

It investigates the application of solid crystallization process in the optimization algorithm.A special way is also proposed for the parameter "stirring" for the target function to get minimum value of the target function in the whole parameters' region.Meanwhile,the optimization algorithm is independent on the initial value of parameters without the larger calculation time.

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.