解轴对称Laplace方程的间接边界积分方程的机械求积法与分裂外推算法  

MECHANICAL QUADRATURE METHODS AND THEIR SPLITTING EXTRAPOLATION FOR SOLVING INDIRECT BOUNDARY INTEGRAL EQUATIONS OF AXISYMMETRIC LAPLACE EQUATIONS

作　　者：李红娥[1] 代振东[2] 朱瑞[3] 

机构地区：[1]西华大学数学与计算机学院,成都610039 [2]四川大学经济学院,成都610064 [3]四川大学数学学院,成都610064

出　　处：《高等学校计算数学学报》2011年第4期319-328,共10页Numerical Mathematics A Journal of Chinese Universities

基　　金：西华大学重点学科-应用数学(XZD0910-09-1)

摘　　要：1引 言函数u∈C2(V)∩ C(V)称为内(外)问题的解,如果u分别满足下面Laplace方程的Dirichlet问题{△u(x)=0,x∈vUVc u(x)=h(x),x∈S这里,x=(x1,x2,x3),V CR3由二维有界连通区域Ω绕z轴旋转而成,S=(O)V是它的边界由分段光滑的曲线Г绕z轴旋转而成,n是V的外单位法向,(V)=VUS,Vc=R3＼(V).对于外问题要求u在无穷远处满足正则性条件,即当｜x｜→∞时,u(x)=O(1/(｜x｜),▽(u(x))=O(1/｜x｜2·根据单层位势理论[3],(1.1)可以转化为第一类的边界积分方程h(x0)=∫s(u)*(x;x0)ρ(x)dS,(ν)x0∈S,这里,ρ(x)是边界S上连续分布的密度函数,(u)*(x;x0)=1/4π｜x- x0｜是三维Laplace方程的基本解,｜x-x0｜表示x和x0之间的距离.By ring potentials, the boundary double integral equation of axisymmetric Laplace equation can be transformed into the indirect boundary single integral equation. By means of the quadrature rules of computing the singular periodic function, mechanical quadrature methods for solving mixed BIEs are presented, which possess high accuracy O（h03） and low computing complexities. Morevoer,using the mutil-parameters asymptotic expansion, we not only improve the accuracy order of the approximation by the splitting extrapolation, but also derive a posteriori error estimation. Numerical examples show that the accuracy order of the approximation high, the extrapolation and posteriori error estimation are effective.

关 键 词：axisymmetric problem Laplace equation indirect boundary integral equation quadrature method splitting extrapolation 

分 类 号：O351.3[理学—流体力学] O175.5[理学—力学]