二维椭圆界面问题的瀑布型多重网格方法  

Cascadic Multigrid Method for Two-dimensional Elliptic Interface Problems

作　　者：董白英[1] DONG Baiying(School of Mathematics and Computer Science, Ningxia Normal University, Guyuan Ningxia 75600)

机构地区：[1]宁夏师范学院数学与计算机科学学院,宁夏固原756000

出　　处：《宁夏师范学院学报》2017年第6期13-20,共8页Journal of Ningxia Normal University

基　　金：宁夏自然科学基金资助项目(NZ15261);宁夏高等学校科学研究资助项目(NGY2016169)

摘　　要：对于二维椭圆界面问题,基于浸入界面有限元方法离散,提出了一类瀑布型多重网格方法.对界面曲线附近的节点,结合界面曲线信息和跳跃条件构造了一类新的高精度插值算子,并基于新插值算子建立瀑布型多重网格法.数值实验说明了新瀑布型多重网格法的稳健性和有效性,并且在相同的迭代终止条件、光滑算子和粗网格算子的条件下,比较了基于四类插值算子的瀑布型多重网格法的收敛速度.New cascadic multigrid is proposed for two-dimensional el liptic interface problems discretized based on the im-mersed finite element method. New higher order operator prolongation is constructed by imposing incorporating the information on the interface and the given jump conditions. In addition,cascadic multigrid methods established by this new interpolation operator. Numerical tests demonstrate the efficiency and robustness of this method. And numerical results of cascadic multigrids based on four types of prolongation are also been shown. Finally,the rates of convergence ofcascadic multigridmethod for four types of interpolation operators are compared in the same conditions （e. g. ,iteration end time,smoothing operator and coarse mesh operator）.

关 键 词：浸入界面有限元法 高精度插值算子 瀑布型多重网格法 

分 类 号：O175.2[理学—数学]