开弧段外Laplace方程单层位势解法探讨  

Simple Layer Potential Method for the Laplace Equation on Open Curves

作　　者：张洁[1] 杨秀文[1] 许川容[1] 

机构地区：[1]后勤工程学院,基础部,重庆,400016

出　　处：《后勤工程学院学报》2005年第1期69-71,共3页Journal of Logistical Engineering University

摘　　要：由Laplace方程Dirichlet问题产生的第一类积分方程的核具有对数奇异性,并且积分方程的解在开弧段端点处具有r-1/2的奇异性.为了克服奇异积分计算的困难,将这种对数奇异性分离出来使用解析积分,其余部分使用数值积分.并用单层位势方法得到该问题解的近似表达式.The kernel of the first integral equation which arises from Dirichlet problem of Laplace equation has a Loga rithmic singularity and the solution for the integral equation has r-1/2 singularity at the endpoints of the open curves. In order to a void this singularity, the kernel is divided into two parts. A special singularity is calculated by exactly integral formula and the other is calculated by numerical integral formula . The solution of approximation formula is obtained by simple layer potential method.

关 键 词：LAPLACE方程 积分方程 奇异性 单层位势 

分 类 号：O241.82[理学—计算数学]