A Dual Super-Element Domain Decomposition Approach for Parallel Nonlinear Finite Element Analysis

This paper presents a new domain decomposition method for nonlinear finite element analysis introducing the concept of dual partition super-elements. The method extends ideas from the displacement frame method and is ideally suited for parallel nonlinear static/dynamic analysis of structural systems. In the new method, domain decomposition is realised by replacing one or more subdomains in a ‘parent system’ each with a placeholder super-element, where the subdomains are processed separately as ‘child partitions’ each wrapped by a dual super-element along the partition boundary. The analysis of the overall system including the satisfaction of equilibrium and compatibility at all partition boundaries is realised through direct communication between all pairs of placeholder and dual superelements. The proposed method has particular advantages for matrix solution methods based on the frontal scheme, and can be readily implemented for existing finite element analysis programs to achieve parallelisation on distributed memory systems with minimal intervention, thus overcoming memory bottlenecks typically faced in the analysis of largescale problems. Several examples are presented in this paper, which demonstrate the computational benefits of the proposed parallel domain decomposition approach and its applicability to the nonlinear structural analysis of realistic structural systems.