Preconditioned conjugate gradient methods for three-dimensional linear elasticity

Finite element modelling of three dimensional elasticity problems gives rise to large sparse matrices. Various preconditioning methods are developed for use in precon-ditioned 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 unstruc-tured tetrahedral meshes. Quadratic basis functions are used. The performance of the iterative methods is compared to a standard direct sparse matrix solver. Problems with up to 70,000 degrees of freedom, and small ( ¿ 1) element aspect ratio are considered