In this paper, Message Passing Interface (MPI) techniques are used to implement high-order full 3-D Navier-Stokes equations in multi-domain applications. A two-domain interface with five-point overlapping used previously is expanded to a multi-domain computation. There are normally two approaches for this expansion. One is to break up the domain into two parts through domain decomposition (say, one overlapping), then using MPI directives to further break up each domain into n parts. Another is to break the domain up into 2n parts with (2n-1) overlappings. In our present effort, the latter approach is used and finite-size overlappings are employed to exchange data between adjacent multi-dimensional sub-domains. It is an alternative way to parallelize the high-order full 3-D Navier-Stokes equations into multi-domain applications without adding much complexity. Results with high-order boundary treatments show consistency among multi-domain calculations and single-domain results.

In parallelizing compilers on distributed memory systems, distributions of irregular sized array blocks are provided for load balancing and irregular problems. The irregular data redistribution is different from the regular block-cyclic redistribution. This paper is devoted to scheduling message for irregular data redistribution that attempt to obtain suboptimal solutions while satisfying the minimal communication costs condition and the minimal step condition. Based on the list scheduling, an efficient algorithm is developed and its experimental results are compared with previous algorithms. The improved list algorithm provides more chance for conflict messages in its relocation phase, since it allocates conflict messages through methods used in a divide-and-conquer algorithm and a relocation algorithm proposed previously. The method of selecting the smallest relocation cost guarantees that the improved list algorithm is more efficient than the other two in average.