求解三维高次拉格朗日有限元方程的代数多重网格法  

AN ALGEBRAIC MULTIGRID METHOD OF THE HIGH ORDER LAGRANGIAN FINITE ELEMENT EQUATION IN R^3

作　　者：孙杜杜[1] 舒适[1] 

机构地区：[1]湘潭大学数学与计算科学学院,湖南湘潭411105

出　　处：《计算数学》2005年第1期101-112,共12页Mathematica Numerica Sinica

基　　金：国家自然科学基金委和中国物理工程研究院联合基金资助(10376031)武器装备预研基金资助.

摘　　要：本文针对带有间断系数的三维椭圆问题,讨论任意四面体剖分下的二次拉格朗日有限元方程的代数多重网格法.通过分析线性和高次有限元空间之间的关系,我们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.进一步,我们还对新的代数多重网格法给出了收敛性分析.数值实验表明这种代数多重网格法对求解二次拉格朗日有限元方程是健壮和有效的.In this paper, we consider a quadratic Lagrangian finite element equation arising from discretizations of 3D elliptic problem with jump coefficients under any tetrahe-dral partition. By analyzing the relationship between the linear finite element space and the high order finite element space, we obtain a new coarsening algorithm and design the corresponding interpolation matrix by applying algebraic approaches. Furthermore, we give an analysis of convergence of our algebraic multigrid algorithm. Numerical experiments show our AMG method is robust and efficient for solving the quadratic Lagrangian finite element system.

关 键 词：拉格朗日 高次 多重网格法 求解 间断系数 有限元空间 代数 有限元方程 三维 剖分 

分 类 号：O241[理学—计算数学]