Hybrid bandwidth minimization with limitable number of starting nodes

Article type: Research Article

Authors: Ondris, L'ubomír

Affiliations: Jantárová 8, 040 01 Košice, Slovakia. E-mail: lubomir.ondris@gmail.com

Abstract: A new hybrid method for minimization of bandwidth and other parameters of large sparse symmetric equation systems is described. The improved efficiency is achieved by a convenient combination of some new techniques: In the first global phase numbering schemas are developed first in usual operating mode from starting node away, then in backward direction as well, in both cases using jumping. A considerable reduction of the CPU-time consumption accompanied by still competitive results can be achieved through eliminating the number of nearby starting nodes. The solution is further improved by a local iterative second phase. Here, local minima are escaped with the help of partial reversing. The performance of the method is evaluated on both artificial and real meshes. Extremely branched artificial meshes for 12 finite element types from structural engineering have been created by a simple uniform algorithm. Minimal bandwidths achieved are given as etalon values for further research. Source code of the artificial mesh generators is freely available. An in-depth evaluation and comparison with the state-of-the-art methods on 45 real meshes from different engineering areas demonstrates the efficiency of the proposed algorithm.

Keywords: Sparse matrix, bandwidth minimization, finite element method, pseudo-peripheral nodes, hybrid renumbering algorithm

DOI: 10.3233/JCM-140511

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 14, no. 6, pp. 347-362, 2014