Numerical Simulation of 3-D Potential Problems by Regular Hybrid Boundary Node Method

Abstract

The Regular Hybrid Boundary Node Method (RHBNM) is developed for solving three-dimensional potential problems. Formulations are developed and a general computer code written in C++. The RHBNM is formulated in terms of the domain and boundary variables. The domain variables are interpolated by classical fundamental solutions with the source points located outside the domain, and the boundary variables are interpolated by MLS approximation. The main idea is to retain the dimensionality advantages of the Boundary Element Method, and localize the integration domain to a regular sub-domain so that no mesh is needed for integration. All integrals can be easily evaluated over regularly shaped domains (in general, semi-sphere in the 3-D problem) and their boundaries. Numerical examples demonstrate that high convergence rate with mesh refinement and high accuracy with a small node number are achievable.

Keywords:

• Meshless Method
• Moving Least-Squares Approximation
• Hybrid Boundary Node Method
• Potential Problem

Acknowledgments

This work is supported by the national 973 program under grant number 2004CB719402 and the program for New Century Excellent Talents in University (NCET-04-0766).