Block Red-Black Ordering: A New Ordering Strategy for Parallelization of ICCG Method

Authors:
Takeshi Iwashita;Masaaki Shimasaki
Affiliations:
Academic Center for Computing and Media Studies, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan. iwashita@media.kyoto-u.ac.jp;Graduate School of Engineering, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan. simasaki@kuee.kyoto-u.ac.jp
Venue:
International Journal of Parallel Programming
Year:
2003

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Abstract

A parallel ordering technique is a typical strategy for parallelization of the ICCG method. This paper proposes a new parallel ordering method to develop a parallel ICCG solver utilizing fewer synchronization points and achieving a high convergence rate. The new parallel ordering is called “block red-black ordering.” In this method, nodes in an analyzed grid are divided into several or many blocks, and red-black ordering is applied to the blocks. Since the blocks with an identical color are independent of each other, forward and backward substitutions in the ICCG iteration can be parallelized in each color. The new method has the advantage that only one synchronization point exists in each parallelized substitution. In order to evaluate the convergence and the parallel speed-up of the method, we carried out an analytical investigation using the ordering graph theory and numerical tests on a scalar parallel computer. The analytical study shows that the convergence rate is improved by an increase in the number of nodes of one block and that an optimal block size for getting the best convergence rate is easily set. The numerical tests show that the new method achieves a high parallel speed-up rate due to fast convergence, small synchronization costs, and effective utilization of the data cache on a scalar parallel computer.