Domain decomposition PCG methods for serial and parallel processing

Abstract

In this paper two domain decomposition formulations are presented in conjunction with the preconditioned conjugate gradient method (PCG) for the solution of large-scale problems in solid and structural mechanics. In the first approach the PCG method is applied to the global coefficient matrix, while in the second approach it is applied to the interface problem after eliminating the internal d.o.f. For both implementations a Subdomain-by-Subdomain (SBS) polynomial pre conditioner is employed based on local information of each sub domain. The approximate inverse of the global coefficient matrix or the Schur complement matrix, which acts as the preconditioner, is expressed by a truncated Neumann series resulting in an additive type local preconditioner. Block type preconditioning, where full elimination is performer inside each block, is also studied and compared with the proposed polynomial preconditioning.