几类典型网格下三维弹性问题的代数多层网格法

ALGEBRAIC MULTIGRID METHODS FOR 3D LINEAR ELASTICITY PROBLEMS ON SOME TYPICAL MESHES

有限元方法是数值求解三维弹性问题的一类重要的离散化方法。在有限元分析中,网格的几何形状及网格质量会对有限元离散代数系统的求解产生很大影响。该文系统研究了几类典型网格对几种常用AMG法计算效率的影响,并进行了详细的性能测试与比较。利用容易获知的部分几何与分析信息(如方程类型,节点自由度信息),再结合经典AMG法中的网格粗化技术,设计了具有更好计算效率和鲁棒性的AMG法。数值试验结果验证了算法的有效性。

Finite element method is one of the most efficient numerical methods for the solution of three-dimensional elasticity problems.In practice,the mesh geometry and mesh quality may have a great effect on the algebraic solvers.In this work,we have presented some numerical studies for evaluating the effectiveness of several commonly used algebraic multigrid（AMG） methods on some typical meshes.We can obtain much more robust and efficient AMG iteration by using the known information that is readily available in most finite element applications,for instance,the type of the partial differential equations（PDEs） considered and the number of physical unknowns residing in each grid,and by combining the coarsening techniques used in the classic AMG method.The efficiency and robustness of the resulting AMG methods are also confirmed by some numerical tests.