无限域拉普拉斯方程问题的高阶边界条件及其应用
High-Order Boundary Conditions for the Problems of Laplace Equation in Infinite Region and Their Application
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摘要: 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.Abstract: The high-order boundary conditions for the problems cf Laplace equation in infinite region have been developed.The improvement in accuracy for numerical solution is achieved by imposing the high-order boundary conditions on the exterior boundarv of a reduced finite region in which the numerical method is used.So both the computing efforts and the required storage in computer are reduced.The numerical examples show that the 1st-order boundary condition approaches to the exact boundary condition and it is clearly superior to the traditional boundary condition and the 2nd-order boundary condition.
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Key words:
- Laplace equation /
- potential function /
- boundary condition /
- conformal transformation
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[1] Bayliss, A., M. Gunzburger, and E. Turke, Boundary conditions for the numerical solution of elliptic equations in exterior regions, SIAM, Appl. Math., 42, 2, April (1982), 430-451. [2] 梁昆森,《数学物理方法》,人民教育出版社,第二版(1987). [3] 黄河宁、李鉴初,散射波的二阶辐射边界条件及其应用,海洋学报,10, 2 (1988), 233-239. -
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