The use of dynamic data structures in finite element applications

Abstract

SUMMARYThe derivation of more efficient algorithms for finite element applications is not the primary goal of this article, but rather the efficient implementation of existing algorithms using dynamic data structures. In some cases the algorithms may be far from optimal, but serve to illustrate the advantages of dynamic data structures. In the first section, a tree data structure termed a PATRICIA tree is described and is shown to be suitable for storing data associated with finite element meshes. The manner in which the tree is constructed guarantees to provide rapid data retrieval times, competitive with those associated with static array data structures, whilst providing the added advantages of a dynamic data structure. The second section introduces a list of lists (LOL) data structure which is used to produce an efficient implementation of an example of a bandwidth reduction algorithm. Furthermore, the LOL data structure is also shown to be appropriate for implementing a novel method for extracting the domain boundary, with its orientation, from a given finite element connectivity matrix.

An algorithm oriented mesh database

“…Maintaining a complete graph that consists of all possible relations between all adjacent mesh entities is, of course, not acceptable in terms of both storage and algorithmic complexity. Some ad hoc data structures have been developed that only maintain speciÿc sets of adjacencies that are able to fulÿll the needs of speciÿc algorithms: mesh generation [1][2][3], mesh reÿnement [4][5][6][7], or solution process [8]. In modern adaptive simulation frameworks, mesh generation, partial di erential equation solving, even post-processing are to be inter-operable components [9].…”

A compact adjacency-based topological data structure for finite element mesh representation

“…A data structure for representing finite element meshes can rely on such constraints to achieve a more compact and adequate topological data structure. Some topological data structures have been specifically designed for attending the needs of particular mesh generation algorithms [24,25] and analysis applications [26]. Beall and Shephard [1] have discussed the need of topology-based mesh representations for finite element applications in a more general form and presented three different proposals.…”

Coarse grain parallel finite element simulations for incompressible flows

“…Therefore, a dynamic data structure is necessary for keeping node-to-element mapping information, which is required for node-based assembly. 24 Naturally, the amount of computation involved in the node-based assembly varies across the di erent nodes. Another implication is related to the synchronization of memory access.…”

“…For an unstructured mesh, however, the number of elements attached to an individual node can be unbounded. Therefore a dynamic data structure is necessary for keeping node-to-element mapping information, which is required for node-based assembly [24]. Naturally, the amount of computation involved in the node-based assembly varies across the different nodes.…”