二维扩散方程边界元解法中的四重奇异积分计算  

The calculation of quadruple singular integral in boundary element method of 2-D diffusion equation

作　　者：吴胤霖[1] 王召刚[1] 

机构地区：[1]91550部队94分队

出　　处：《信息技术》2009年第5期196-199,共4页Information Technology

摘　　要：对二维热传导方程的Dirichlet初边值问题,采用带时间变量的基本解,利用基于单层位势的间接边界积分方程及其等价的Galerkin变分形式求解,该方法涉及到与时空相关的四重奇异积分的计算。在采用常单元离散的情况下,推导了具体实施数值计算所需的积分公式,完成了数值实验,验证了该方法的有效性和可行性。Dirichlet problem of two-dimensional diffusion equation is considered. By adopting time-dependent fundamental solution, indirect boundary integral equation and its equivalent Galerkin variational formula which based on simple layer potential is conducted for the equation. The method comes down to quadruple singular integral calculation on space-time. On condition that the equation is discretizated by adopting constant cell, integral formulas needed by actualizing numerical calculation are deduced. Finally, the numerical examples illustrate the feasibility and the efficiency of the proposed method.

关 键 词：扩散方程 Galerkin边界元法 间接边界积分方程 奇异积分 

分 类 号：O241.82[理学—计算数学]