求解非结构四边形二次拉格朗日有限元方程的代数多重网格法

An Algebraic Multigrid Method of Quadratic Lagrangian Finite Element Equations Under the Unstructured Quadrilateral Grids

针对一类带间断系数的椭圆边值问题,在非结构四边形部分下,讨论了两种二次拉格朗日有限元方程的代数多重网格法,通过利用双线性元和二次元基函数之间的表示关系,给出了一种新的网格粗化算法和构造提升算子的代数途径.数值实验表明:新的AMC法具有更好的“鲁棒”性和效率.

For a class of Quadratic finite element diseretization systems of an elliptic boundary problem with jump coefficients under the unstructured quadrilateral grids,we are concerned with two kinds of Quadratic Lagrangian finite element equations, by analyzing the relationship between the linear finite element and Quadratic finite element basis functions, a new AMG method is designed. The numerical results show that our new AMG method is more robust and efficient.