A new meshless regular local boundary integral equation (MRLBIE) approach

A new meshless method based on a regular local integral equation and the moving least-squares approximation is developed. The present method is a truly meshless one as it does not need a ` nite element or boundary element meshʹ, either for purposes of interpolation of the solution variables, or for the integration of the `energyʹ. All integrals can be easily evaluated over regularly shaped domains (in general, spheres in three- dimensional problems) and their boundaries. No derivatives of the shape functions are needed in constructing the system sti ness matrix for the internal nodes, as well as for those boundary nodes with no essential- boundary-condition-prescribed sections on their local boundaries. Numerical examples presented in the paper show that high rates of convergence with mesh re nement are achievable, and the computational results for the unknown variable and its derivatives are very accurate. No special post-processing procedure is required to compute the derivatives of the unknown variable, as the original result, from the moving least-squares approximation, is smooth enough.