The meshless standard and hypersingular boundary node methods-Applications to error estimation and adaptivity in three-dimensional problems

The standard (singular) boundary node method (BNM) and the novel hypersingular boundary node method (HBNM) are employed for the usual and adaptive solutions of three-dimensional potential and elasticity problems. These methods couple boundary integral equations with moving least-squares interpolants while retaining the dimensionality advantage of the former and the meshless attribute of the latter. The 'hypersingular residuals', developed for error estimation in the mesh-based collocation boundary element method (BEM) and symmetric Galerkin BEM by Paulino et al., are extended to the meshless BNM setting. A simple 'a posteriori' error estimation and an effective adaptive refinement procedure are presented. The implementation of all the techniques involved in this work are discussed, which includes aspects regarding parallel implementation of the BNM and HBNM codes. Several numerical examples are given and discussed in detail. Conclusions are inferred and relevant extensions of the methodology introduced in this work are provided.