It provides an overview of the parallel computing for 2-dimensional plasma simulations with particle clouds in cells methods under both shared-memory and distrbuted-memory parallel computing environments.The parallel algorithm and its implementation are desigened on the basis of the serial algorithm and the executing characteristics of the serial code.The practical parallel computations are performed under Challenge,DAWN 1000+, Power PC Cluster and XMZY. Many important conclusions are given and quite useful for the parallel computations of both types of particle simulation methods and other applicational codes.

It presents the AGE(Alternating Group Explicit) method for solving the two-dimensional Burgers equation.The method is unconditionally stable by analysis of linearization procedure and has obvious property of parallelism.Numerical example is given at the shared memory computer.

The Block ADI(Alternating Direction Implicit) method for solving the two-dimensional convection diffusion equation is developed in this paper.The Block ADI method is unconditionally stable and has the localization property of both computation and communication,so the method can be used on the massively parallel processing system with distributed memory processors.The numerical example is given on a parallel system of networks of work stations.

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.

An alternating segment Crank-Nicholson method for the diffusion equation is constructed.The method is unconditionally stable and has the obvious property of parallelism.Numerical results for an example show this new method has satisfactory.

This paper describes the experiences on vectorization and parallelization of te code YGX for te two-dimensional fluid dynamics at super computer YH-1 and YH-2, and gives some results of numerical experiments concerning the speed up on the computers.

The parallel algorithms for solving the implicit difference equations have been studied in the paper. The basic idea is to divide the system of difference equations into a set of subsystems which can be solved in parallel. The direct method and iterative method are given and the convergence theorem on the iteration is proved. To show the efficiency of the segment implicit iteration, the papper gives the numerical experiment for an example of the diffusion equation.