求解二维扩散方程的加权平均隐式多重网格方法  

Multigrid Solution Based on Weighted Average Implicit Scheme of the Two Dimensional Diffusion Equation

作　　者：葛永斌[1] 吴文权[1] 卢曦[1] 

机构地区：[1]上海理工大学动力工程学院,上海200093

出　　处：《内蒙古大学学报（自然科学版）》2003年第5期490-494,共5页Journal of Inner Mongolia University：Natural Science Edition

基　　金：国家自然科学基金资助项目(59876023);上海市教委青年基金资助项目(02QG22)

摘　　要：提出了数值求解二维扩散方程两种精度分别为O(τ2+h2)和O(τ2+h4)的无条件稳定的加权平均隐格式,并采用多重网格方法进行求解,从而克服了传统迭代法在求解隐格式时收敛速度慢的缺陷,提高了求解效率.数值实验验证了该方法的精确性和可靠性.Two classes of unconditional stable,weighted average implicit difference schemes for the twodimensional diffusion equation are proposed.Their local truncation errors are O(τ2+h2) and O(τ2+h4) respectively.A multigrid technique is employed to accelerate the convergence speed of traditional relaxation methods and fast solutions are obtained.Numerical experiment is carried out to prove their accuracy and dependability.

关 键 词：扩散方程 多重网格 加权平均隐格式 无条件稳定 

分 类 号：O241.82[理学—计算数学]