The meshless hypersingular boundary node method for three-dimensional potential theory and linear elasticity problems

Citation
Mk. Chati et al., The meshless hypersingular boundary node method for three-dimensional potential theory and linear elasticity problems, ENG ANAL, 25(8), 2001, pp. 639-653
Citations number
68
Categorie Soggetti
Engineering Mathematics
Journal title
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
ISSN journal
09557997 → ACNP
Volume
25
Issue
8
Year of publication
2001
Pages
639 - 653
Database
ISI
SICI code
0955-7997(200109)25:8<639:TMHBNM>2.0.ZU;2-F
Abstract
The Boundary Node Method (BNM) represents a coupling between Boundary Integ ral Equations (BIEs) and Moving Least Squares (MLS) approximants. The main idea here is to retain the dimensionality advantage of the former and the m eshless attribute of the latter. The result is a 'meshfree' method that dec ouples the mesh and the interpolation procedures. The BNM has been applied to solve 2-D and 3-D problems in potential theory and linear elasticity. Th e Hypersingular Boundary Element Method (HBEM) has diverse important applic ations in areas such as fracture mechanics, wave scattering, error analysis and adaptivity, and to obtain a symmetric Galerkin boundary element formul ation. The present work presents a coupling of Hypersingular Boundary Integ ral Equations (HBIEs) with MLS approximants, to produce a new meshfree meth od-the Hypersingular Boundary Node Method (HBNM). Numerical results from th is new method, for selected 3-D problems in potential theory and in linear elasticity, are presented and discussed in this paper. (C) 2001 Elsevier Sc ience Ltd. All rights reserved.