Efficient iterative solution of constrained finite element analyses

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

doi:10.1016/s0045-7825(97)00286-7

Cited by 14 publications

(13 citation statements)

References 12 publications

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“…By substituting Equation (7) into Equation (6), that is, by static condensation, the following equation is derived for the interface DOFs:…”

Section: (K)mentioning

confidence: 99%

Incorporation of multipoint constraints into the balancing domain decomposition method and its parallel implementation

Miyamura

2006

Numerical Meth Engineering

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SUMMARYThe domain decomposition method (DDM) is a major solution algorithm that is used to parallelize the finite element method. In the case of implicit structural analysis using the DDM, the substructuring-based iterative linear solver is a powerful tool when an effective preconditioner such as the balancing domain decomposition (BDD) method is used. In the present study, a method by which to incorporate a set of linear multipoint constraints (MPC) into the BDD method is proposed. In this method, when an MPC is enforced on the internal degrees of freedom (DOFs) in some subdomains, the DOFs are converted into interface DOFs, that is, all of the DOFs constrained by MPCs become interface DOFs. Then, the interface problem with the set of MPCs for the interface DOFs is solved by the conjugate projected gradient method. In order to combine the above procedure with the preconditioner used in the BDD method, the effect of the MPCs for the interface DOFs is also imposed on the coarse grid problem of the BDD method using the penalty method. A parallel implementation of the present method is also described. Some illustrative examples are solved and good convergence and parallel performance of the present method are demonstrated.

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“…By substituting Equation (7) into Equation (6), that is, by static condensation, the following equation is derived for the interface DOFs:…”

Section: (K)mentioning

confidence: 99%

Incorporation of multipoint constraints into the balancing domain decomposition method and its parallel implementation

Miyamura

2006

Numerical Meth Engineering

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“…The approach used for projecting the constrained system into a reduced space is described in a paper by Saint-Georges et al [21] and is briefly summarized here.…”

Section: Constraint Reductionmentioning

confidence: 99%

SIERRA framework version 4 : solver services.

Williams¹

2005

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Several SIERRA applications make use of third-party libraries to solve systems of linear and nonlinear equations, and to solve eigenproblems. The classes and interfaces in the SIERRA framework that provide linear system assembly services and access to solver libraries are collectively referred to as solver services. This paper provides an overview of SIERRA's solver services including the design goals that drove the development, and relationships and interactions among the various classes. The process of assembling and manipulating linear systems will be described, as well as access to solution methods and other operations. 3 AcknowledgementThe format of this report is based on information found in [17] and the example material at [2].4

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“…Several approaches have been developed for these problems, given a solver for the primal matrix K, namely Uzawa's method [4], D R A F T projection methods [18] and Schur elimination (or static condensation techniques). These methods decouple the primal and dual equations, and though they are useful and have their place in the repertoire of methods for solving these problems, they all suffer some shortcomings (eg, not general, scalable, robust, or costly).…”

Section: Introductionmentioning

confidence: 99%

Algebraic multigrid methods for constrained linear systems with applications to contact problems in solid mechanics

Adams

2004

Numerical Linear Algebra App

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SUMMARYThis article develops a general framework for applying algebraic multigrid techniques to constrained systems of linear algebraic equations that arise in applications with discretized PDEs. We discuss constraint coarsening strategies for constructing multigrid coarse grid spaces and several classes of multigrid smoothers for these systems. The potential of these techniques is investigated with their application to contact problems in solid mechanics.

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Efficient iterative solution of constrained finite element analyses

Cited by 14 publications

References 12 publications

Incorporation of multipoint constraints into the balancing domain decomposition method and its parallel implementation

Incorporation of multipoint constraints into the balancing domain decomposition method and its parallel implementation

SIERRA framework version 4 : solver services.

Algebraic multigrid methods for constrained linear systems with applications to contact problems in solid mechanics

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