Meshless standard and hypersingular boundary node methods: Applications in three-dimensional potential theory and linear elasticity

The Boundary Node Method (BNM) and the Hypersingular Boundary Node Method (HBNM) are developed in this work for solving problems in potential theory and linear elasticity. The BNM and HBNM represent a coupling between Boundary Integral Equations (BIEs) and Moving Least Squares (MLS) interpolants. The main idea here is to retain the dimensionality advantage of the former and the meshless attribute of the later. This results in decoupling of the "mesh" and the interpolation procedure for the field variables.; A general purpose BNM and HBNM computer code (serial and parallel), for 3D problems in potential theory and linear elasticity, has been developed. Several parameters involved in the meshless method need to be chosen carefully for the successful implementation of the method. An in-depth and systematic study has been carried out in order to better understand the effects of the various parameters on the performance of the proposed meshless method. Since the proposed meshless method is quite computer intensive, a parallel version of the serial code is developed in this work.; The hypersingular residuals, developed for error estimation in the mesh-based collocation Boundary Element Method (BEM), 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 techniques involved in this work are discussed and several numerical examples for adaptive analysis are given and discussed in detail.