Extending substructure based iterative solvers to multiple load and repeated analyses

Farhat, Charbel; Crivelli, Luis; Roux, F. X.

doi:10.1016/0045-7825(94)90083-3

Cited by 85 publications

(71 citation statements)

References 7 publications

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“…This is because the complexity of solving a system of equations arising from one step of an implicit structural dynamic (large time-step) analysis, or from a static analysis, is essentially the same. For the optimization of FETI to the solution of repeated systems arising form the linear dynamic analysis or the eigenvalue analysis of a structure, we refer the reader to [10,20,21]. For both benchmark problems, we equip FETI with the topological scaling matrix W(").…”

Section: Preliminary Scalability Resultsmentioning

confidence: 99%

“…have the same material and discretization properties as subdomain s 2 ( ' ) , then WcS)(i) = l / m (see Section 2), which shows that the topological scaling overviewed in Section 2 is a particular case of the superlumped stiffness scaling summarized in Eq. (21). In [19], using a set of model problems and a few realistic ones, it was shown that the FETI method equipped with the stiffness scaling matrix W(') specified in Eq.…”

Section: U(q)(jq) In the Neighboring Subdomain Q ( Q ) Then W(')(i)mentioning

confidence: 99%

“…The size of this coarse problem increases with the number of subdomains. Initially, it was advocated to solve the FETI coarse problems iteratively, using a CG algorithm that is optimized for the solution of problems with repeated right hand-sides [20,21]. That approach was motivated by the fact that the CG method requires only matrix-vector products that can be performed in parallel at the subdomain level, and which necessitate only short range communication between neighboring subdomains.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Massively Parallel Sparse Eigensolver for Structural Dynamics Finite Element Analysis

Day¹,

Reese²

1999

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Section: Preliminary Scalability Resultsmentioning

confidence: 99%

Section: U(q)(jq) In the Neighboring Subdomain Q ( Q ) Then W(')(i)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Massively Parallel Sparse Eigensolver for Structural Dynamics Finite Element Analysis

Day¹,

Reese²

1999

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“…The "many query" limit has certainly received considerable attention: from "fast loads" or multiple right-hand side notions (e.g. [5,7]) to matrix perturbation theories (e.g. [1,25]) to continuation methods (e.g.…”

Section: Introduction To Reduced Basis Output Bound Methodsmentioning

confidence: 99%

“…It is also possible to ask for a specific Problem and Output using the following command in MATLAB: st2m --model fin3d --output Troothowever it implies that one knows the name of the Problem and Output. Then, to set the values for the seven components of the parameter vector, we enter p.values (1) (6).name='t'; p.values(7).value=2.5; p.values (7).name='L'; within the MATLAB command window. To determine the output value and bound gap for this value of the 7-tuple parameter, we then enter To be more certain that Troot was truly greater than 1.05, we could easily ask for those values of t for which s N − ∆ N ≥ 1.05; again readily effected by a simple function call.…”

Section: Simlabmentioning

confidence: 99%

A Mathematical and Computational Framework for Reliable Real-Time Solution of Parametrized Partial Differential Equations

Prud'Homme¹,

Rovas²,

Veroy³

et al. 2002

ESAIM: M2AN

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Abstract. We present in this article two components: these components can in fact serve various goals independently, though we consider them here as an ensemble. The first component is a technique for the rapid and reliable evaluation prediction of linear functional outputs of elliptic (and parabolic) partial differential equations with affine parameter dependence. The essential features are (i) (provably) rapidly convergent global reduced-basis approximations -Galerkin projection onto a space WN spanned by solutions of the governing partial differential equation at N selected points in parameter space; (ii) a posteriori error estimation -relaxations of the error-residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs of interest; and (iii) off-line/on-line computational procedures -methods which decouple the generation and projection stages of the approximation process. This component is ideally suited -considering the operation count of the online stage -for the repeated and rapid evaluation required in the context of parameter estimation, design, optimization, and real-time control. The second component is a framework for distributed simulations. This framework comprises a library providing the necessary abstractions/concepts for distributed simulations and a small set of tools -namely SimT E X and SimLaB-allowing an easy manipulation of those simulations. While the library is the backbone of the framework and is therefore general, the various interfaces answer specific needs. We shall describe both components and present how they interact.Mathematics Subject Classification. 65N15, 65N30, 68U01, 68U20, 68M14, 68M15.

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Coarse grain parallel finite element simulations for incompressible flows

Grant

Webster

Zhang

1998

Int. J. Numer. Meth. Engng.

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Parallel simulation of incompressible uid ows is considered on networks of homogeneous workstations. Coarse-grain parallelization of a Taylor-Galerkin=pressure-correction ÿnite element algorithm are discussed, taking into account network communication costs. The main issues include the parallelization of system assembly, and iterative and direct solvers, that are of common interest to ÿnite element and general numerical computation. The parallelization strategies are implemented on a Sun workstation cluster using the Parallel Virtual Machine (PVM) message passing library. Test results are obtained with a maximum of nineteen workstations and various PVM conÿgurations are exhibited. Parallel e ciency close to ideal has been achieved for some strategies adopted. It is suggested that load balancing may not always be beneÿcial on distributed platforms with broadcasting communication connection. ? 1998 John Wiley & Sons, Ltd.

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Extending substructure based iterative solvers to multiple load and repeated analyses

Cited by 85 publications

References 7 publications

A Massively Parallel Sparse Eigensolver for Structural Dynamics Finite Element Analysis

A Massively Parallel Sparse Eigensolver for Structural Dynamics Finite Element Analysis

A Mathematical and Computational Framework for Reliable Real-Time Solution of Parametrized Partial Differential Equations

Coarse grain parallel finite element simulations for incompressible flows

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