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

Abstract

The Boundary Node Method (BNM) represents a coupling between Boundary Integral Equations (BIEs) and Moving Least Squares (MLS) approximants. The main idea here is to retain the dimensionality advantage of the former and the meshless attribute of the latter. The result is a ‘meshfree’ method that decouples 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. The Hypersingular Boundary Element Method (HBEM) has diverse important applications in areas such as fracture mechanics, wave scattering, error analysis and adaptivity, and to obtain a symmetric Galerkin boundary element formulation. The present work presents a coupling of Hypersingular Boundary Integral Equations (HBIEs) with MLS approximants, to produce a new meshfree method — the Hypersingular Boundary Node Method (HBNM). Numerical results from this new method, for selected 3-D problems in potential theory and in linear elasticity, are presented and discussed in this paper.