Block Red-Black Ordering Method for Parallel Processing of ICCG Solver

The present paper proposes a new parallel ordering, ”block red-black ordering,” for a parallelized ICCG solver with fewer synchronization points and a high convergence rate. In the new method, nodes in an analyzed grid are divided into several or many blocks, and red-black ordering is applied to the blocks. Several blocks are assigned to each processor and the substitution is carried out in parallel. Only one synchronization point exists in each parallelized substitution. We performed an analytical investigation using the ordering graph theory and computational tests on a scalar parallel computer. These results show that a convergence rate is improved by an increase in the number of nodes of one block and that a high parallel performance is attained by using an appropriate block size.