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| An algebraic multigrid method for a class of discrete models of lattice structures |
| Revised:May 05, 2003 |
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| DOI：10.7511/jslx20052036 |
| KeyWord:lattice structure,discrete model,algebraic multigrid,preconditioning,approximately continuous model |
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| Abstract: |
| A new type of algebraic multigrid (AMG) methods are designed to find the solution of the discrete models possessing some special properties corresponding to lattice structures. The selection of coarser grids and the construction of interpolation operators based on element agglomeration and energy optimization are discussed in detail. The methods are suitable to the large-scale numerical computations for lattice structure of two dimension. At the same time, a preconditioned conjugate gradient method with AMG as a preconditioner (AMG-CG) is obtained. Numerical results have shown that the constructed AMG and AMG-CG methods are highly efficient and robust. In addition, the approximately continuous models of lattice structure provide some theoretical basis for the reliability of the AMG algorithm and the veracity of computational results. |
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