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 infinite region hare been developed. The improvement in accuracy for numerical solution is achieved by imposing the high-order boundary conditions on the exterior boundary of a reduced finite region in which the numerical method is used. So both computing efforts and the required storage in computer are reduced. The numer-leal examples show that the lst-order boundary conditien approaches to the exact boundary condition and it is clearly superior to the traditional boundary condition and the 2nd-order boundary condition.