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

Ferronato, Massimiliano; Pini, Giorgio; Gambolati, Giuseppe

doi:10.1002/nag.729

Cited by 21 publications

(21 citation statements)

References 44 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The linear system 1 is solved by a preconditioned SQMR algorithm, which has proved one of the most efficient Krylov subspace methods for coupled consolidation problems [37,56], using a unit vector b as the right-hand side and the following exit test on the real relative residual:…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Typically, K and C are SPD, with C incorporating the time integration step t. The ill-conditioning of the discretized equations arises from the unbalancing between the magnitude of the C and K entries and depends on the t size [36]. For more details, such as the explicit expression of K, B, and C, along with their conditioning and structure, see for instance [37].…”

Section: The Paricp Algorithm For Fe-coupled Consolidationmentioning

confidence: 99%

See 1 more Smart Citation

Parallel inexact constraint preconditioning for ill-conditioned consolidation problems

2012

Self Cite

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

Section: Numerical Resultsmentioning

confidence: 99%

Section: The Paricp Algorithm For Fe-coupled Consolidationmentioning

confidence: 99%

Parallel inexact constraint preconditioning for ill-conditioned consolidation problems

2012

Self Cite

View full text Add to dashboard Cite

show abstract

“…As far as the approximation of S −1 is concerned, a quite natural option is performing an incomplete triangular factorization of S. This gives rise to the so-called inexact constraint preconditioner (ICP) recently discussed in [21]. In the FE discretization of the coupled consolidation equations with a suitable nodal numbering, a block symmetric indefinite linear system arises where A 11 is the structural stiffness matrix and A 22 is the flow time-dependent matrix, with A 11 positive definite and A 22 negative definite (see for a discussion Reference [8]). Replacing in (2) and ( 11 is approximated by AINV, even though the overall ICP performance in realistic problems is not very dissimilar from that obtained with stabilized ILU-type preconditioners [21].…”

Section: Block Constraint Preconditioners Consider a Symmetric (2×2)-mentioning

confidence: 99%

“…Equation (8) shows that MCP can be efficiently applied to a vector via a sequence of backward and forward substitutions. The quality of M −1 as a preconditioner for A can be evaluated through the eigenspectrum of the preconditioned matrix M −1 A, i.e.…”

Section: −1mentioning

confidence: 99%

Performance and robustness of block constraint preconditioners in finite element coupled consolidation problems

Ferronato¹,

Bergamaschi²,

Gambolati³

2009

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

Block constraint preconditioners are a most recent development for the iterative solution to large-scale, often ill-conditioned, coupled consolidation problems. A major limitation to their practical use, however, is the somewhat difficult selection of a number of user-defined parameters (at least 4) in a more or less optimal way. The present paper investigates the robustness of three variants of the block constraint preconditioning in relation to the above parameters. A theoretical analysis of the eigenspectrum of the preconditioned matrix provides relatively simple bounds of the eigenvalues as a function of these parameters. A number of test problems used to validate the theoretical results show that both the mixed constraint preconditioner (MCP) combined with the symmetric quasi-minimal residual (SQMR) solver and the MCP triangular variant (T-MCP) combined with the bi-conjugate gradient stabilized (Bi-CGSTAB) are efficient and robust tools for the solution to difficult Finite Element-discretized coupled consolidation problems. Moreover, the practical selection of the user-defined parameters is relatively easy as a stable behavior is observed for a wide range of fill-in degree values. The theoretical bounds on the eigenspectrum of the preconditioned matrix may help to suggest the most appropriate parameter combination

show abstract

“…Although the final coefficient matrix may take on different forms, i.e. symmetric indefinite, unsymmetric indefinite or unsymmetric positive definite [22], the first structure is to be generally preferred and is actually more often used. The corresponding block or two-level matrix A reads as…”

Section: Introductionmentioning

confidence: 99%

Preconditioners in computational geomechanics: A survey

Gambolati

Ferronato

Janna

2011

Num Anal Meth Geomechanics

View full text Add to dashboard Cite

The finite element (FE) solution of geomechanical problems in realistic settings raises a few numerical issues depending on the actual process addressed by the analysis. There are two basic problems where the linear solver efficiency may play a crucial role: 1. fully coupled consolidation and 2. faulted uncoupled consolidation. A class of general solvers becoming increasingly popular relies on the Krylov subspace (or Conjugate Gradient-like) methods, provided that an efficient preconditioner is available. For both problems mentioned above, the possible preconditioners include the diagonal scaling (DS), the Incomplete LU decomposition (ILU), the mixed constraint preconditioning (MCP) and the multilevel incomplete factorization (MIF). The development and the performance of these algorithms have been the topic of several recent works. The present paper aims at providing a survey of the preconditioners available to date in computational geomechanics. In particular, a review and a critical discussion of DS, ILU, MCP and MIF are given along with some comparative numerical results

show abstract

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

Cited by 21 publications

References 44 publications

Parallel inexact constraint preconditioning for ill-conditioned consolidation problems

Parallel inexact constraint preconditioning for ill-conditioned consolidation problems

Performance and robustness of block constraint preconditioners in finite element coupled consolidation problems

Preconditioners in computational geomechanics: A survey

Contact Info

Product

Resources

About