A fast implementation of the FETI-DP method: FETI-DP-RBS-LNA and applications on large scale problems with localized non-linearities

As parallel and distributed computing gradually becomes the computing standard for large scale problems, the domain decomposition method (DD) has received growing attention since it provides a natural basis for splitting a large problem into many small problems, which can be submitted to individual computing nodes and processed in a parallel fashion. This approach not only provides a method to solve large scale problems that are not solvable on a single computer by using direct sparse solvers but also gives a flexible solution to deal with large scale problems with localized non-linearities. When some parts of the structure are modified, only the corresponding subdomains and the interface equation that connects all the subdomains need to be recomputed. In this paper, the dual-primal finite element tearing and interconnecting method (FETI-DP) is carefully investigated, and a reduced back-substitution (RBS) algorithm is proposed to accelerate the time-consuming preconditioned conjugate gradient (PCG) iterations involved in the interface problems. Linear-non-linear analysis (LNA) is also adopted for large scale problems with localized non-linearities based on subdomain linear-non-linear identification criteria. This combined approach is named as the FETI-DP-RBS-LNA algorithm and demonstrated on the mechanical analyses of a welding problem. Serial CPU costs of this algorithm are measured at each solution stage and compared with that from the IBM Watson direct sparse solver and the FETI-DP method. The results demonstrate the effectiveness of the proposed computational approach for simulating welding problems, which is representative of a large class of three-dimensional large scale problems with localized non-linearities. Copyright © 2005 John Wiley & Sons, Ltd.