无限域拉普拉斯方程问题的高阶边界条件及其应用

对无限域Laplace方程问题,推导出了高阶边界条件.在采用数值方法的有限域的外边界上应用高阶边界条件,可以在保证计算精度的前提下缩小数值求解域,从而减小计算工作量和少占用计算机内存.数值算例表明,一阶边界条件近似于精确边界条件,它明显地优于经典边界条件和二阶边界条件.     

High-order boundary conditions for the problems of Laplace equation in infinite region and their application

The high-order boundary conditions for the problems of Laplace equation in infiniteregion have been developed.The improvement in accuracy for numerical solution isachieved by imposing the high-order boundary conditions on the exterior boundary of areduced finite region in which the numerical method is used.So both the computing effortsand the required storage in computer are reduced.The numerical examples show that thelst-order boundary condition approaches to the exact boundary condition and it is clearlysuperior to the traditional boundary condition and the2nd-order boundary condition.