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A study of the efficiency of iterative methods for linear problems in structural mechanics
Author(s) -
Samuelsson A.,
Wiberg NE.,
Bernspång L.
Publication year - 1986
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.1620220115
Subject(s) - iterative method , relaxation (psychology) , conjugate gradient method , factorization , gaussian elimination , mathematics , finite element method , incomplete lu factorization , matrix (chemical analysis) , successive over relaxation , mathematical optimization , gaussian , computer science , matrix decomposition , algorithm , structural engineering , materials science , physics , engineering , local convergence , psychology , social psychology , eigenvalues and eigenvectors , quantum mechanics , composite material
Abstract The efficiency of iterative methods in linear structural mechanics is studied. The efficiency concerns the calculation time, the numerical accuracy and the core storage needed. We state that iterative methods are effective in connection with hierarchical improvement of a primary approximation. Three iterative methods are studied: the conjugate gradient method preconditioned by a modified incomplete factorization matrix, the same method preconditioned by a matrix obtained from natural factors on elemental level, and a Jacobi integration preconditioned by viscous relaxation split in an element‐by‐element way. We make comparisons with direct methods, Gaussian elimination and factorization by use of natural factors.