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Preconditioned conjugate gradient methods for three‐dimensional linear elasticity
Author(s) -
Dickinson J. K.,
Forsyth P. A.
Publication year - 1994
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620371305
Subject(s) - conjugate gradient method , finite element method , solver , polygon mesh , mathematics , iterative method , degrees of freedom (physics and chemistry) , quadratic equation , mathematical optimization , sparse matrix , elasticity (physics) , linear elasticity , algorithm , computer science , geometry , structural engineering , physics , materials science , quantum mechanics , engineering , composite material , gaussian
Finite element modelling of three‐dimensional elasticity problems give 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 a standard direct sparse matrix solver. Problems with up to 70 000 degrees of freedom and small (≪1) element aspect ratio are considered.