关键词: 近似逆, 预条件, 迭代法, 异构并行计算, GPU集群

Abstract: This paper shows the study on the parallel algorithm of AINV (approximate inverse) and SSOR-AI (symmetric successive over relaxation approximate inverse) preconditioners on GPU cluster systems. With multilevel k-way graph partitioning, this paper proposes the parallel method which can transform a sparse matrix into block arrow form based on a method to identify interior/boundary vertex of subgraphs and a permutation. Based on the block arrow matrix, with the strategy of sequential computation approximate inverse of inner block and parallel computation between the different blocks, the parallel algorithm of AINV and SSOR-AI is obtained. Based on the optimization techniques of collaborative computing between CPU and GPU, page-locked host memory and overlapping transfers with computation on device, this paper combines parallel approximate inverse preconditioner with CG (conjugate gradient) algorithm to obtain a hybrid parallel solver for linear systems. Numerical experiments indicate that applying the above methods can obtain very good acceleration effect and scalability both AINV parallel implementation and SSOR-AI parallel implementation on cluster-GPU.

Key words: approximate inverse, preconditioner, iterative method, heterogeneous parallel computing, GPU cluster