各向异性板应力集中问题有限元方程的预处理方法

A Preconditioned Method for the Finite Element Equation of the Stress Concentration Problem in Anisotropic Plate

针对各向异性板应力集中问题有限元方程的数值求解,建立了一类简单且实用的代数多重网格预处理共轭梯度法(AMG -CG法) .由于该预处理方法能有效地降低刚度矩阵的条件数,使刚度矩阵的谱分布更集中,从而大大地提高了计算效率.数值结果表明,AMG -CG法对求解应力集中问题有限元方程是十分有效和健壮的。

In this paper we construct a simple but applicable algebraic multigrid-preconditioned CG algorithm (AMG-CG ) for the solution of the finite element equation of the stress concentration problem in anisotropic plate. Since this method can reduce the condition number of the stiffness matrix, it is effective for the solution of the stress concentration problem. Numerical results have shown that the constructed AMG-CG method is very efficient and robust.