无界区域各向异性椭圆边值问题的一种Schwarz交替法  

A Schwarz Alternating Method for the Anisotropic Elliptic Boundary Value Problem on Unbounded Domains

作　　者：郑权[1] 董俊雨[1] 白荣霞[1] 

机构地区：[1]北方工业大学理学院,北京100144

出　　处：《工程数学学报》2009年第3期489-498,共10页Chinese Journal of Engineering Mathematics

基　　金：北京市自然科学基金(1072009);国家重点基础研究发展计划项目(2002CB312104)

摘　　要：本文研究一种求解无界区域各向异性椭圆边值问题的基于有限元法和自然边界元法的Schwarz交替法,通过引入椭圆人工边界解决长条形边界外区域无界性并克服小系数困难,根据投影理论得到在1-范数意义下的几何收敛性,由Fourier分析得到迭代收敛速度的依赖于子区域交叠程度、准确解最低频率和各向异性系数的最优表达式。数值实例印证上述收敛理论,并表现这类实际应用。This paper investigates a Schwarz alternating method, based on the finite element method and the natural boundary element method, for solving the anisotropic elliptic problem on unbounded domains. The domain infinity outside the elongated boundary is resolved and the difficulty of the small coefficient is overcome by introducing elliptic artificial boundaries. Its geometric convergence is proved in the sense of 1-norm by using the projection theory. The Fourier analysis is used to derive an optimal convergence rate formula dependent upon the overlapping degree of subdomains, the lowest frequency of the exact solution and the anisotropic coefficients. The numerical examples confirm the convergence theory and show their practical application.

关 键 词：无界区域 各向异性椭圆边值问题 重叠型区域分解法 有限元法 自然边界归化 

分 类 号：O241.4[理学—计算数学]