Theoretical comparison of the FETI and algebraically partitioned FETI methods, and performance comparisons with a direct sparse solver

Rixen, Daniel J.; Farhat, Charbel; Tezaur, Radek; Mandel, Jan

doi:10.1002/(sici)1097-0207(19991010)46:4<501::aid-nme685>3.0.co;2-7

Cited by 55 publications

(11 citation statements)

References 33 publications

(34 reference statements)

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“…Using an automatic mesh decomposer [29,30], a given finite element structural model is first decomposed into N , 2 Np subdomains, where Np denotes the target number of processors. The potential advantages of generating more subdomains than there are processors are discussed in [14,31], among other references. Next, the generated subdomains are re-arranged into Np clusters containing each one or several subdomains, and each cluster is assigned to one processor.…”

Section: Implementation Of Salinas and Feti O N Massively Parallel DImentioning

confidence: 99%

A Massively Parallel Sparse Eigensolver for Structural Dynamics Finite Element Analysis

Day¹,

Reese²

1999

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Section: Implementation Of Salinas and Feti O N Massively Parallel DImentioning

confidence: 99%

A Massively Parallel Sparse Eigensolver for Structural Dynamics Finite Element Analysis

Day¹,

Reese²

1999

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“…By simple parallel solver , it is meant to be similar to the 1991 FETI static solver or its equivalents in terms of implementation overhead and the correspondingly comparable solution efficiency. This paper presents one such a simple parallel algorithm that, when used for dynamic analysis, is labeled as the AFETI‐EI algorithm .…”

Section: Introductionmentioning

confidence: 99%

A simple explicit–implicit finite element tearing and interconnecting transient analysis algorithm

González

Park

2011

Numerical Meth Engineering

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SUMMARYA simple explicit-implicit finite element tearing and interconnecting (FETI) algorithm (AFETI-EI algorithm) is presented for partitioned transient analysis of linear structural systems. The present algorithm employs two decompositions. First, the total system is partitioned via spatial or domain decomposition to obtain the governing equations of motions for each partitioned domain. Second, for each partitioned subsystem, the governing equations are modally decomposed into the rigid-body and deformational equations. The resulting rigid-body equations are integrated by an explicit integrator, for its stability is not affected by step-size restriction on account of zero-frequency contents (! D 0). The modally decomposed partitioned deformation equations of motion are integrated by an unconditionally stable implicit integration algorithm. It is shown that the present AFETI-EI algorithm exhibits unconditional stability and that the resulting interface problem possesses the same solution matrix profile as the basic FETI static problems. The present simple dynamic algorithm, as expected, falls short of the performance of the FETI-DP but offers a similar performance of implicit two-level FETI-D algorithm with a much cheaper coarse solver; hence, its simplicity may offer relatively easy means for conducting parallel analysis of both static and dynamic problems by employing the same basic scalable FETI solver, especially for research-mode numerical experiments. Copyright

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“…In this paper, the scalable domain decomposition (DD)-based finite element tearing and interconnecting dual-primal (FETI-DP) method [8][9][10][11][12][13], which is an enhanced variant of the ubiquitous iterative FETI solver [10,[14][15][16][17][18][19][20][21][22][23][24][25][26][27], is proposed as an incomplete block-diagonal preconditioning solver for Equation (1). It is equipped with the Krylov reusage technique first proposed in [15,16] for accelerating its convergence for systems with multiple and repeated right-hand sides.…”

Section: Introductionmentioning

confidence: 99%

A FETI‐preconditioned conjugate gradient method for large‐scale stochastic finite element problems

Ghosh

Avery

Farhat

2009

Numerical Meth Engineering

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SUMMARYIn the spectral stochastic finite element method for analyzing an uncertain system, the uncertainty is represented by a set of random variables, and a quantity of interest such as the system response is considered as a function of these random variables. Consequently, the underlying Galerkin projection yields a block system of deterministic equations where the blocks are sparse but coupled. The solution of this algebraic system of equations becomes rapidly challenging when the size of the physical system and/or the level of uncertainty is increased. This paper addresses this challenge by presenting a preconditioned conjugate gradient method for such block systems where the preconditioning step is based on the dual-primal finite element tearing and interconnecting method equipped with a Krylov subspace reusage technique for accelerating the iterative solution of systems with multiple and repeated right-hand sides. Preliminary performance results on a Linux Cluster suggest that the proposed solution method is numerically scalable and demonstrate its potential for making the uncertainty quantification of realistic systems tractable.

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Theoretical comparison of the FETI and algebraically partitioned FETI methods, and performance comparisons with a direct sparse solver

Cited by 55 publications

References 33 publications

A Massively Parallel Sparse Eigensolver for Structural Dynamics Finite Element Analysis

A Massively Parallel Sparse Eigensolver for Structural Dynamics Finite Element Analysis

A simple explicit–implicit finite element tearing and interconnecting transient analysis algorithm

A FETI‐preconditioned conjugate gradient method for large‐scale stochastic finite element problems

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