Parallelization of ICCG Method Using Three Dimensional Block Red-Black Ordering Method

Abstract

The present paper deals with parallelization of ICCG method. A reordering (parallel ordering) technique is one of typical parallel processing techniques of ICCG method. While several parallel orderings have been proposed, the block red-black ordering that is proposed by the authors is relatively new ordering. This ordering method has advantages in convergence rate and in synchronization costs, and its effectiveness was confirmed in a preliminary numerical test for 2-d finite difference analyses. In the present paper, this method is enhanced for 3-d finite difference analyses, which require more computational efforts than 2-d analyses. We here describe the details of the implementation procedure of the block red-black ordering in 3-d analyses. Numerical tests for a 3-d partial differential equation problem are performed. It is shown that 3-d block red-black ordering method attains high parallel efficiency due to fast convergence and effective use of data cache.