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
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.