二维热传导方程的Dirichlet初边值问题的Galerkin边界元计算方法  

Galerkin Boundary Element Method for Dirichlet Problem of 2D Heat Conduction

作　　者：吴胤霖[1] 祝家麟[1] 汪学海[1] 张永兴[2] 

机构地区：[1]重庆大学数理学院,重庆400044 [2]重庆大学土木工程学院,重庆400045

出　　处：《四川师范大学学报（自然科学版）》2009年第4期427-431,共5页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(50679097)资助项目

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,完成了数值算例,验证了该方法的有效性和可行性.Dirichlet problem of two-dimensional heat conduction equation is considered. By adopting time-dependent fundamental solution, indirect boundary integral equation and its equivalent Galerkin variational formula which is based on simple layer potential a solving method is conducted for the equation. The method is involved with quadruple integral calculation on space-time. On the condi- tion that the equation is discretizated by adopting constant cell, the integral formulas needed by actualizing numerical calculation are deduced. Finally, numerical examples are given to illustrate the feasibility and the efficiency of the proposed method.

关 键 词：热传导方程 Galerkin边界元法 间接边界积分方程 单层位势 

分 类 号：O241.82[理学—计算数学]