Problem-dependent preconditioners for iterative solvers in FE elastostatics

Saint-Georges, Pascal; Warzée, Guy; Notay, Yvan; Beauwens, Robert

doi:10.1016/s0045-7949(98)00277-6

Cited by 17 publications

(8 citation statements)

References 13 publications

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“…Preconditioners based on diagonally compensated reduction give good results on moderately ill-conditioned problems, such as certain solid elasticity problems [258] and diffusion problems posed on highly distorted meshes [32], but are ineffective for more difficult problems arising from the finite element analysis of thin shells and other structures [32,172,259].…”

Section: The Symmetric Positive Definite Casementioning

confidence: 99%

Preconditioning Techniques for Large Linear Systems: A Survey

Benzi¹

2002

Journal of Computational Physics

1,011

659

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This article surveys preconditioning techniques for the iterative solution of large linear systems, with a focus on algebraic methods suitable for general sparse matrices. Covered topics include progress in incomplete factorization methods, sparse approximate inverses, reorderings, parallelization issues, and block and multilevel extensions. Some of the challenges ahead are also discussed. An extensive bibliography completes the paper. c 2002 Elsevier Science (USA)

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Section: The Symmetric Positive Definite Casementioning

confidence: 99%

Preconditioning Techniques for Large Linear Systems: A Survey

Benzi¹

2002

Journal of Computational Physics

1,011

659

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“…ILU-type and IC-type preconditioners have been developed and successfully implemented in various fields, e.g. [6,[31][32][33]. In coupled consolidation problems, they have proved robust and efficient in combination with a proper scaling technique [34].…”

Section: Introductionmentioning

confidence: 99%

The role of preconditioning in the solution to FE coupled consolidation equations by Krylov subspace methods

Ferronato¹,

Pini²,

Gambolati³

2008

Num Anal Meth Geomechanics

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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

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“…A different algorithm is proposed in [27] where the incomplete factor is obtained through a matrix-orthogonalization instead of a Cholesky decomposition. In the present paper we use the strategy discussed in [28] that has proved promising in structural mechanics applications [3,29]. Following this approach, we can write…”

Section: Positive Definiteness Of S I11mentioning

confidence: 99%

“…Though different choices are possible, e.g. [28,29], the option = = −|s 1 j | is particularly attractive because in such a way the sum of the absolute value of the arbitrarily introduced entries | |+| | is minimal. Applying the same procedure to the other dropped entries of L i+1 gives rise to a factorization that is guaranteed to be the exact factorization of a SPD matrix:…”

Section: Positive Definiteness Of S I11mentioning

confidence: 99%

Multi‐level incomplete factorizations for the iterative solution of non‐linear finite element problems

Janna

Ferronato

Gambolati

2009

Numerical Meth Engineering

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Several engineering applications give rise quite naturally to linearized FE systems of equations possessing a multi-level structure. An example is provided by geomechanical models of layered and faulted geological formations. For such problems the use of a multi-level incomplete factorization (MIF) as a preconditioner for Krylov subspace methods can prove a robust and efficient solution accelerator, allowing for a fine tuning of the fill-in degree with a significant improvement in both the solver performance and the memory consumption. The present paper develops two novel MIF variants for the solution of multi-level symmetric positive definite systems. Two correction algorithms are proposed with the aim of preserving the positive definiteness of the preconditioner, thus avoiding possible breakdowns of the preconditioned conjugate gradient solver. The MIF variants are experimented with in the solution of both a single system and a long-term quasi-static simulation dealing with a multi-level geomechanical application. The numerical results show that MIF typically outperforms by up to a factor 3 a more traditional algebraic preconditioner such as an incomplete Cholesky factorization with partial fill-in. The advantage is emphasized in a longterm simulation where the fine fill-in tuning allowed for by MIF yields a significant improvement for the computer memory requirement as well

show abstract

Problem-dependent preconditioners for iterative solvers in FE elastostatics

Cited by 17 publications

References 13 publications

Preconditioning Techniques for Large Linear Systems: A Survey

Preconditioning Techniques for Large Linear Systems: A Survey

The role of preconditioning in the solution to FE coupled consolidation equations by Krylov subspace methods

Multi‐level incomplete factorizations for the iterative solution of non‐linear finite element problems

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