Please use this identifier to cite or link to this item: https://doi.org/10.1002/nag.662
Title: Comparison between iterative solution of symmetric and non-symmetric forms of Biot's FEM equations using the generalized Jacobi preconditioner
Authors: Toh, K.-C. 
Phoon, K.-K. 
Keywords: Biot's consolidation equations
Generalized Jacobi preconditioner
Non-symmetric linear systems
Issue Date: 25-Jun-2008
Source: Toh, K.-C., Phoon, K.-K. (2008-06-25). Comparison between iterative solution of symmetric and non-symmetric forms of Biot's FEM equations using the generalized Jacobi preconditioner. International Journal for Numerical and Analytical Methods in Geomechanics 32 (9) : 1131-1146. ScholarBank@NUS Repository. https://doi.org/10.1002/nag.662
Abstract: Finite element discretization of Biot's consolidation equations can produce a symmetric indefinite system (commonly used in geomechanics) or a non-symmetric system. While this difference appears to be minor, however, it will require the selection of entirely different Krylov subspace solvers with potentially significant impact on solution efficiency. The former is solved using the symmetric quasi-minimal residual whereas the latter is solved using the popular bi-conjugate gradient stabilized. This paper presents an extensive comparison of the symmetric and non-symmetric forms by varying the time step, size of the spatial domain, choice of physical units, and left versus left-right preconditioning. The generalized Jacobi (GJ) preconditioner is able to handle the non-symmetric version of Biot's finite element method equation, although there are no practical incentives to do so. The convergence behaviour of GJ-preconditioned systems and its relation to the spectral condition number or the complete spectrum are studied to clarify the concept of ill-conditioning within the context of iteration solvers. Copyright © 2007 John Wiley & Sons, Ltd.
Source Title: International Journal for Numerical and Analytical Methods in Geomechanics
URI: http://scholarbank.nus.edu.sg/handle/10635/65314
ISSN: 03639061
DOI: 10.1002/nag.662
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