On the Treatment of Neumann Boundary Conditions in Collocation-Based Meshless Methods
The existence of Neumann boundary is a major cause of the poor accuracy and instability of collocation-based methods. Taking a Poisson equation with Neumann boundary condition as the model, the present paper studies the effects of two different radial point interpolation shape functions and their parameters on the accuracy of numerical solutions of the equation. We also study the effects of methods including fictious point method, nodes densification method and Hermite collocation method on the improvement of numerical accuracy. By comparison of analytic and numerical solutions computed using a program developed during research, we obtain parameters of shape functions and methods of treatment of Neumann boundary conditions that can be adopted to give better numerical accuracy.
Laijiu Zheng, Shin-ichi Kuroda, Huawu Liu, Bing Du, Ju Wei and Yuping Zhao
X. D. Zhang et al., "On the Treatment of Neumann Boundary Conditions in Collocation-Based Meshless Methods", Applied Mechanics and Materials, Vols. 423-426, pp. 1757-1762, 2013