【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.更多还原

【Abstract】 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 condition 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.更多还原