Multicolor SOR Method with Consecutive Memory Access Implementation in a Shared and Distributed Memory Parallel Environment

摘要

A new implementation of the multicolor SOR was proposed including the variable sorting to achieve consecutive memory access. Its effect was confirmed on a shared memory vector/parallel and SMP machines, and it was found that the multicolor SOR method with consecutive memory access demonstrates excellent performance on both types of machine. The CMA multicolor SOR method retains almost the same convergence rate of the original SOR method and its execution speed is much faster than the original SOR on a vector computer. On the other hand, the parallel performance on a vector/parallel machine was greatly improved by one-dimensional serialization of the array, which leads to excellent load balance between cores. On an SMP machine, the CMA code showed the best performance among the test codes. In addition, good scalability was confirmed up to 256 nodes using a medium size of 416 x 416 x 416 for all tested methods in a distributed memory parallel environment. Especially, for the strong scaling test case, the CMA code showed super-linear behavior for a small number of CPUs compared with the other methods. Thus, if the size of the problem becomes bigger as the number of CPUs increases, i.e., the weak scaling case, then scalability seems to be promising.