多搜索方向共轭梯度法——一种无需整体内积的共轭梯度类方法

MULTIPLE SEARCH DIRECTION CONJUGATE GRADIENT METHOD:A GLOBAL INNER PRODUCT FREE CONJUGATE GRADIENT-TYPE METHOD

§1.引言 许多大型科学与工程计算问题都归结为大型稀疏线性方程组的求解,因此,在高性能并行计算机高速发展的今天,面向并行计算环境研究大型稀疏线性方程组的高效并行算法显得尤为重要.

In this paper, we proposed a new CG-type method based on domain decomposition method, which is called multiple search direction conjugate gradient (MSD-CG) method. In each iteration, it uses a search direction in each subdomain. Instead of making all search directions conjugate to each other, as in block CG method, we require that they are nonzero in one subdomain only. An approximate version of MSD-CG method only requires communication between neighboring subdomains and eliminate global inner product entirely. This method is therefore well suited for massively parallel computation. Numerical experiments on Dawning 3000 and P-II Cluster show the efficiency of our method and that it compares favorably with other domain decomposition method.