椭圆边界上的自然积分算子及各向异性外问题的耦合算法  

NATURAL INTEGRAL OPERATOR ON ELLIPTIC BOUNDARY AND THE COUPLING METHOD FOR AN ANISOTROPIC PROBLEM

作　　者：余德浩[1] 贾祖朋[1] 

机构地区：[1]中国科学院数学与系统科学研究院

出　　处：《计算数学》2002年第3期375-384,共10页Mathematica Numerica Sinica

基　　金：国家重点基础研究专项经费(G19990328);中国科学院数学与系统科学研究院创新经费资助项目.

摘　　要：1.引 言为求解微分方程的外边值问题常需要引进人工边界（见[1-4]）,对人工边界外部区域作自然边界归化得到的自然积分方程即Dirichlet-Neumann映射,正是人工边界上的准确的边界条件（见[2-6]）,这是一类非局部边界条件.自然积分算子即Dirichlet-Neumann算子,In this paper, the natural integral operator(D-N operator) and natural boundary element method for harmonic problem over exterior elliptic domain are discussed. Based on this ,the natural boundary reduction for a kind of exterior problem of anisotropic elliptic equation with constant coefficients is studied, the natural integral equation and its solution on circular and elliptic boundaries are obtained. These results can be directly applied to coupling method and domain decomposition methods for exterior boundary value problem. Especially, when the problem is over an exterior domain of a slender obstacle , these methods are more effective.

关 键 词：各向异性外问题 自然积分算子 椭圆边界 耦合算法 微分方程 外边值问题 

分 类 号：O241[理学—计算数学]