Algebraic multigrid method for higher-order finite element equations in three dimensional linear elasticity
Received:February 21, 2009  Revised:October 09, 2009
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KeyWord:algebraic multigrid  higher-order elements  3D elasticity problems  tetrahedron partition
肖映雄 湘潭大学 土木工程与力学学院, 湘潭 ;湘潭大学 数学与计算科学学院,湘潭
张红梅 湖南工业大学 理学院,株洲
舒适 湘潭大学 数学与计算科学学院,湘潭
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      As for finite element method, the higher-order elements are often used in that they are superior and necessary under certain conditions over the low-order ones, for example, they can overcome the Poisson’s ratio locking. However, they have much higher computational complexity than the linear elements. In this paper, we firstly introduce this method for elliptic problems, to the solution of three dimensional elasticity problems discretized using higher-order elements and propose a two-level method by algebraic approaches. With the existing algebraic multigrid(L_AMG) method used as a solver on the first coarse level, an AMG method is then designed for high-order discretizations. The results of various numerical experiments show that the resulting AMG method is more robust and efficient for the solution of higher-order finite element equations in three dimensional linear elasticity.