A new graph representation for cable-membrane structures

In this paper, a new graph representation is proposed which is applicable to cable-membrane structures modelled using both one- and two-dimensional elements. The proposed graph representation is an engineering design approach and not based on a mathematically derived representation. The proposed graphs are partitioned using state-of-the-art tools, including METIS [METIS, a software package for partitioning unstructured graphs, partitioning meshes, and computing fill-reducing orderings of sparse matrices (1997); J Parallel Distribut Comput (1997)], and JOSTLE [Advances in computational mechanics with parallel and distributed processing (1997); Parallel dynamic graph-partitioning for unstructured meshes (1997); Int J High Perform Comput Appl 13 (1999) 334; Appl Math Model 25 (2000) 123]. The graph representation performs better than standard graph representations for those cases when the rules of geometric locality and uniform element distribution around nodes are violated. The relation of the proposed graph representation to the most advanced hypergraph representation [IEEE Trans Parallel Distribut Syst 10 (1999) 673; Parallel Comput 26 (2000) 673] is also discussed.