A scalable parallel algorithm especially for large-scale three dimensional simulations with seriously non-uniform molecular distributions is presented. In particular, based on cell-block data structures, this algorithm uses space filling curve to convert three-dimensional domain decomposition for load distribution across processors into one-dimensional load balancing problems for which run-time measurement-based multilevel averaging weights method can be applied successfully. Parallel numerical experiments for simulations of three-dimensional metal-eject physical models with 210 million particles using 500 processors of one massively parallel processors have shown that this algorithm has achieved speedup about 420.

Discussion is given on the domain decomposition parallel iterative algorithm,which is aimed at the implicit difference equation under 3-D Cartesian coordination and the error estimates for both the serial and the parallel iteration are provided.The analysis and comparison about the numerical results indicate that the parallel iterative algorithm is highly parallelizable and scalable.

With the development of massively parallel processing, it is necessary that the parallel applications would be capable of good scalability. It is described how to use the near optimal scalability analysis method with the two dimensional electromagnetic plasma parallel program using particle in cell method as an example. Having known the performance of small parallel systems, one can obtain the information about how many processors which the larger systems are running on can obtain the more"reasonable" performance when using the near optimal scalability analysis. A suit of practical scalability evaluation method is also proposed to find the reason why the practical scalability is bad, and help to optimize the application programs.

On the basis of the message passing parallel programming platform MPI,and with the high performance characteristics of contemporary microprocessors,it describes the parallelization and optimization for a two dimensional molecular dynamics code(MDP) to simulate the high speed collision physical model problems.The serial optimization has shown to be of double performance improvements,and the parallel efficiencies being above 90% under the cluster consisted of 8 Pentium-Ⅱ microprocessors.

By the design of new parallel algorithm and the organization of grid mapping, a serial code Lared-Ⅰ has been successfully parallelized for numerical simulations of 2-dimension three temperature hydrodynamics with the message passing programming environment. Moreover, a dynamic load balance method is also designed according to the physical and the code executing characteristics, which can significantly improve the parallel performance. The numerical results under both parallel computing environments are given as well.

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.