Preconditioned conjugate gradient methods for three-dimensional linear elasticity. (English) Zbl 0806.73066
Summary: Finite element modelling of three-dimensional elasticity problems gives rise to large sparse matrices. Various preconditioning methods are developed for use in preconditioned conjugate gradient iterative solution techniques. Incomplete factorizations based on levels of fill, drop tolerance, and a two-level hierarchical basis are developed. Various techniques for ensuring that the incomplete factors have positive pivots are presented. Computational tests are carried out for problems generated using unstructured tetrahedral meshes. Quadratic basis functions are used. The performance of the iterative methods is compared to the standard direct sparse matrix solver. Problems with up to 70 000 degrees of freedom and small \((<<1)\) element aspect ratio are considered.
MSC:
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 74B05 | Classical linear elasticity |
| 65F10 | Iterative numerical methods for linear systems |
| 65F50 | Computational methods for sparse matrices |
Keywords:
incomplete factorizations; quadratic basis functions; drop tolerance; two-level hierarchical basis; unstructured tetrahedral meshesSoftware:
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