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

Abstract

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.

Mesoscale partitioned analysis of brick-masonry arches

“…In order to overcome this intrinsic limitation, mesoscale masonry descriptions have been coupled with macroscale models based on a simple sequential quadratic programming (SQP) approach [26] achieving accurate results in the analysis of realistic curved masonry structures. In the proposed numerical description for large masonry arches, the novel computational strategy for brick\block masonry recently proposed in [42] is considered, where the mesoscale description is incorporated within an advanced partitioning approach previously developed at Imperial College [43][44][45] which. The adoption of a mesoscale partitioned approach guarantees exactly the same accuracy of the 3D mesoscale description at structural scale, achieving exceptional computational benefits through parallelisation on High Performance…”

“…The proposed approach for modelling masonry arches adopts the mesoscale description of masonry [29] combined with partitioned modelling [43][44][45], both of which were previously implemented in ADAPTIC [30], a general FE program for nonlinear structural analysis.…”

“…As pointed out in previous research [42,46], this detailed modelling strategy may necessitate an excessive computational effort when applied to the analysis of large structure as in the analysis of wide multi-ring brick-masonry arches. In this case to guarantee computational efficiency, the full mesoscale description can be combined with the partitioning approach allowing for parallel computation previously developed at Imperial College [43][44][45], thus providing an accurate and efficient numerical strategy.…”

“…The computational efficiency provided by the use of the partitioning approach developed previously at Imperial College [43][44][45] and applied here to the analysis of the large brick-masonry arch is investigated. The computational cost associated with different partitioning strategies has been analysed in the case of elastic analysis, where a patch load P = 20kN was applied onto the arch in five steps.…”

“…the most efficient model is characterised by the highest speed-up). In modelling the arch, both flat and hierarchic partitioning techniques [42][43][44][45][46] are considered. The former strategy is a single level partitioning approach, where the masonry arch is represented by a parent structure consisting of super-elements which model partitioned subdomains.…”