The Meshless Local Boundary Equation Method

摘要

A method similar to the local boundary integral equation method that preserves its properties and is free from singular integrals is proposed. The approach is based on selection of the weighting functions from a homogeneous solution of the problem rather than the fundamental solution. Many examples of 2D Laplace and Helmholtz equations and 3D vector wave equation are presented for verification. The method shows optimistic performance over piece-wise smooth boundaries. Radial basis functions of thin plate spline type are used for meshless discretization. The dependable performance of the proposed method provides a hopeful applicability to numerical solutions of partial differential equations.