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| Preconditioning methods for discrete models of two types of lattice structures |
| Received:August 20, 2010 Revised:January 04, 2011 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx20121020 |
| KeyWord:lattice structures preconditioner algebraic multigrid condition numbers approximately continuous equations |
| Author | Institution |
| 肖映雄 |
湘潭大学 土木工程与力学学院, 湘潭 |
| 陈鹏 |
湘潭大学 数学与计算科学学院, 湘潭 |
| 舒适 |
湘潭大学 数学与计算科学学院, 湘潭 |
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| Abstract: |
| In this paper,we propose two kinds of preconditioning methods for the discrete models of lattice structures with 3 or 4 reference nodes.One is the block preconditioned conjugate gradient method (BPCG) with a block diagonal inverse as a preconditioner,and another is the preconditioning GMRES method (PGMRES) based on the block lower triangular inverse as a preconditioner.The numerical results show that the BPCG method is of good efficiency and robustness for the lattice structures with 3 reference nodes,but for honeycomb lattices,especially when α is very small,the efficiency of this method becomes poor.In this case,the PGMRES method is best both in the calculation of the stability and CPU times.In order to improve the efficiency of the inner iterations,we use the PCG method with GAMG preconditioner based on scalar elliptic problems to find the inverse of each sub-block matrix.In addition,the approximately continuous models of lattice structure provide some theoretical basis for the reliability of the inner iterations. |
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