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The role of preconditioning in the solution to FE coupled consolidation equations by Krylov subspace methods
Author(s) -
Ferronato Massimiliano,
Pini Giorgio,
Gambolati Giuseppe
Publication year - 2008
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.729
Subject(s) - krylov subspace , preconditioner , consolidation (business) , generalized minimal residual method , finite element method , subspace topology , mathematics , linear system , block (permutation group theory) , computer science , mathematical optimization , mathematical analysis , engineering , geometry , structural engineering , accounting , business
The repeated solution in time of the linear system arising from the finite element integration of coupled consolidation equations is a major computational effort. This system can be written in either a symmetric or an unsymmetric form, thus calling for the implementation of different preconditioners and Krylov subspace solvers. The present paper aims at investigating when either a symmetric or an unsymmetric approach should be better used. The results from a number of representative numerical experiments indicate that a major role in selecting either form is played by the preconditioner rather than by the Krylov subspace method itself. Two other important issues addressed are the size of the time integration step and the possible lumping of the flow capacity matrix. It appears that ad hoc block constrained preconditioners provide the most robust algorithm independently of the time step size, lumping, and symmetry. Copyright © 2008 John Wiley & Sons, Ltd.

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