【摘要】 本文分析了求解依时问题的边界元法的三种途径:采用依时基本解作为权函数,在时间和空间上进行积分;利用积分交换,将依时问题变换成一系列边值问题求解,再进行逆变换;边界元与有限差分相结合,可得到一系列时间步长上的边值问题,通过求解这一系列边值问题而得到解序列,在此基础上,提出了用加权残值法(WRM)导出了一类依时问题的边界元-差分法新公式.由于在该公式中权函数的选取极为自由,因而避免了求控制微分方程基本解的困难.同时,公式中的所有短阵均为常短阵,只需形成一次,故可节省计算时间.更多还原

【Abstract】 In this paper,the authors first briefly analyse three kinds of element methods for solving time-dependent problems:the integration method,the integration transform method and the method of boundary element couplingwith finite difference (BEM-FDM).Based on which,a new type of BEM-FDM for time-dependent problems is developed by means of weighted residual method.Since there is no limitation to the selection of the weig-hted functions,the fundamental solution of the governing equation needs not be found.Besides,every matrix,in the formulations is constant so that they need only be formed for once and the computing time can be saved.更多还原