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.

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