A geometric-based algebraic multigrid method for higher-order finite element equations in two-dimensional linear elasticity

作者：Xiao, Yingxiong; Shu, Shi^*; Zha, Tuyan

来源：Numerical Linear Algebra with Applications, 2009, 16(7): 535-559.

DOI：10.1002/nla.629

• algebraic multigrid method
• higher-order elements
• plane strain problem
• unstructured grid

In this paper, we will discuss the geometric-based algebraic multigrid (AMG) method for two-dimensional linear elasticity problems discretized using quadratic and cubic elements. First, a two-level method is proposed by analyzing the relationship between the linear finite element space and higher-order finite element space. And then a geometric-based AMG method is obtained with the existing solver used as a solver on the first coarse level. The resulting AMG method is applied to some typical elasticity problems including the plane strain problem with jumps in Young's modulus. The results of various numerical experiments show that the proposed AMG method is much more robust and efficient than a classical AMG solver that is applied directly to the high-order systems alone. Moreover, we present the corresponding theoretical analysis for the convergence of the proposed AMG algorithms. These theoretical results are also confirmed by some numerical tests.

• 出版日期2009-7
• 单位湖南工程学院; 湘潭大学