无网格Chebyshev配点法求解二维位势问题

Meshless Chebyshev Collocation Method for Solving Two-dimensional Potential Problems

基于Chebyshev正交多项式插值理论和无网格配点技术,提出一种新型的无网格数值离散方法,称之为Chebyshev配点法.所提方法采用Chebyshev多项式的零点(Gauss-Lobatto节点)为插值节点,可最大限度地降低龙格现象,并且提供插值多项式的最佳一致逼近.数值算例表明,本文算法稳定,效率高,并可达到很高的计算精度.

In this study,a new framework for the numerical solutions of two-dimensional(2D)potential problems is presented.A Chebyshev collocation scheme(CCS)is introduced for the efficient and accurate approximation of particular solution for the given 2D boundary value problem.We collocate the numerical scheme at the Gauss-Lobatto nodes to ensure the pseudo-spectral convergence of the Chebyshev interpolation.Two benchmark numerical examples in both smooth and piecewise smooth 2D geometries are presented to demonstrate the applicability and efficiency of the proposed method.