| Abstract: | In this article, 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 the block CG method O'Leary, D. P. (1980). The block conjugate gradient algorithm and related methods. Lin. Alg. Appl., 29, 293–322.], we require that they are nonzero in corresponding subdomains only. The GIPF-CG method, an approximate version of the 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. We give some propositions and a preconditioned version of the MSD-CG method. |
