A modified SSOR preconditioner for sparse symmetric indefinite linear systems of equations

Chen, X.; Toh, Kim-Chuan; Phoon, Kok‐Kwang

doi:10.1002/nme.1461

Cited by 38 publications

(25 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Consolidation problems are solved via a time-stepping approach and there are several examples of studies which examine the link between time step size and ill-conditioning [21,22]. Others have concentrated on simple preconditioners derived from the standard Jacobi or SSOR methods in conjunction with the symmetric quasi-minimal residual (QMR) method [23,24].…”

mentioning

confidence: 99%

Element‐based preconditioners for elasto‐plastic problems in geotechnical engineering

Augarde

Ramage²,

Staudacher

2006

Numerical Meth Engineering

View full text Add to dashboard Cite

SUMMARYIterative solvers are widely regarded as the most efficient way to solve the very large linear systems arising from finite element models. Their memory requirements are small compared to those for direct solvers. Consequently, there is a major interest in iterative methods and particularly the preconditioning necessary to achieve rapid convergence. In this paper we present new element-based preconditioners specifically designed for linear elasticity and elasto-plastic problems. The study presented here is restricted to simple associated plasticity but should find wide application in other plasticity models used in geotechnics.

show abstract

mentioning

confidence: 99%

Element‐based preconditioners for elasto‐plastic problems in geotechnical engineering

Augarde

Ramage²,

Staudacher

2006

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

“…(Note that ILU0 preconditioner is symmetric for the symmetric Biot's equation.) In this section, we demonstrate that the same advantage holds also for the ILU0-preconditioned symmetric system arising from the finite element method (FEM) discretization of a simple footing problem resting on a heterogeneous soil medium (details are described in Section 3.2 of [17]). …”

Section: Gj Versus Ilu0 Preconditioningmentioning

confidence: 71%

Comparison between iterative solution of symmetric and non‐symmetric forms of Biot's FEM equations using the generalized Jacobi preconditioner

Toh

Phoon

2007

Num Anal Meth Geomechanics

View full text Add to dashboard Cite

SUMMARYFinite 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.

show abstract

“…The issue of preconditioning for the FE coupled consolidation equations has been addressed in a number of recent and less recent works, including Jacobi and over-relaxed linear iterations, e.g., [38,39]; stabilized global incomplete factorizations, e.g., [40]; and block preconditioners, e.g., [8,9]. For a recent survey, see [41].…”

Section: The Paricp Algorithm For Fe-coupled Consolidationmentioning

confidence: 99%

Parallel inexact constraint preconditioning for ill-conditioned consolidation problems

2012

View full text Add to dashboard Cite

Constraint preconditioners have proved very efficient for the solution of ill-conditioned finite element (FE) coupled consolidation problems in a sequential computing environment. Their implementation on parallel computers, however, is not straightforward because of their inherent sequentiality. The present paper describes a novel parallel inexact constraint preconditioner (ParICP) for the efficient solution of linear algebraic systems arising from the FE discretization of the coupled poro-elasticity equations. The ParICP implementation is based on the use of the block factorized sparse approximate inverse incomplete Cholesky preconditioner, which is a very recent and effective development for the parallel preconditioning of symmetric positive definite matrices. The ParICP performance is experimented with in real 3D coupled consolidation problems, proving a scalable and efficient implementation of the constraint preconditioning for highperformance computing. ParICP appears to be a very robust algorithm for solving ill-conditioned large-size coupled models in a parallel computing environment

show abstract

A modified SSOR preconditioner for sparse symmetric indefinite linear systems of equations

Cited by 38 publications

References 26 publications

Element‐based preconditioners for elasto‐plastic problems in geotechnical engineering

Element‐based preconditioners for elasto‐plastic problems in geotechnical engineering

Comparison between iterative solution of symmetric and non‐symmetric forms of Biot's FEM equations using the generalized Jacobi preconditioner

Parallel inexact constraint preconditioning for ill-conditioned consolidation problems

Contact Info

Product

Resources

About