解半线性抛物问题的瀑布型多重网格法的最优性  

The optimality of applying cascadic multigrid method for solving semilinear parabolic problems

作　　者：郭晓君[1] 李荣军[2] 李大治[1] 高岩波[1] 

机构地区：[1]南通大学理学院,江苏南通226007 [2]湖南工程学院数理系,湖南湘潭411105

出　　处：《扬州大学学报（自然科学版）》2013年第2期16-20,共5页Journal of Yangzhou University：Natural Science Edition

基　　金：国家自然科学基金资助项目(61273103);南通市科技计划资助项目(BK2012072)

摘　　要：将瀑布型多重网格法推广到半线性抛物问题,证明了以Richardson迭代为光滑子时二维半线性抛物型边值问题的瀑布型多重网格法在能量范数下可获得最优收敛阶,同时分析了计算工作量,得到工作量的最优性或拟最优性.The author extends the utilization of cascadic multigrid method to the resolution of semilinear parabolic problems.It is proved that this method does help to attain the optimal convergence order to solve the 2-D semilinear parabolic problems within the energy norm when using Richardson iteration as smoothing operator.At the same time,it analyzes the computational complexity when using this method,with the optimality or quasi-optimality of the computation demonstrated in this paper as well.

关 键 词：半线性抛物问题 瀑布型多重网格法 Richardson迭代 最优性 

分 类 号：O241.82[理学—计算数学]