Enhanced balancing Neumann-Neumann preconditioning in computational fluid and solid mechanics

SUMMARYIn this work, we propose an enhanced implementation of balancing Neumann–Neumann (BNN) preconditioning together with a detailed numerical comparison against the balancing domain decomposition by constraints (BDDC) preconditioner. As model problems, we consider the Poisson and linear elasticit...

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Bibliographic Details
Published in:International journal for numerical methods in engineering Vol. 96; no. 4; pp. 203 - 230
Main Authors: Badia, Santiago, Martín, Alberto F., Príncipe, Javier
Format: Journal Article
Language:English
Published: Chichester Blackwell Publishing Ltd 26.10.2013
Wiley
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Subjects:
Algebra
Algorithms
balancing domain decomposition
BDDC
BNN
coarse-grid correction
Computation
Computational methods in fluid dynamics
Dirichlet problem
Domain decomposition
Elasticity
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Linear and multilinear algebra, matrix theory
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Numerical analysis. Scientific computation
parallelization
Physics
Preconditioning
scalability
Sciences and techniques of general use
Solid mechanics
Solvers
Static elasticity (thermoelasticity...)
Structural and continuum mechanics
Three dimensional
Performance evaluation
BNN
Constraint
elasticity
Grid
coarse-grid correction
Modeling
scalability
Distributed memory
Inverse matrix
Linear elasticity
Tridimensional elasticity
Dirichlet problem
Vibration control
BDDC
Conjugate gradient method
Singular matrix
Neumann problem
Balancing
Pseudoinverse
Poisson equation
parallelization
Boundary value problem
balancing domain decomposition
Large scale
Domain decomposition
Shared memory
Preconditioning
Structural analysis
ISSN:0029-5981, 1097-0207
Online Access:Get full text
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Summary:SUMMARYIn this work, we propose an enhanced implementation of balancing Neumann–Neumann (BNN) preconditioning together with a detailed numerical comparison against the balancing domain decomposition by constraints (BDDC) preconditioner. As model problems, we consider the Poisson and linear elasticity problems. On one hand, we propose a novel way to deal with singular matrices and pseudo‐inverses appearing in local solvers. It is based on a kernel identification strategy that allows us to efficiently compute the action of the pseudo‐inverse via local indefinite solvers. We further show how, identifying a minimum set of degrees of freedom to be fixed, an equivalent definite system can be solved instead, even in the elastic case. On the other hand, we propose a simple implementation of the algorithm that reduces the number of Dirichlet solvers to only one per iteration, leading to similar computational cost as additive methods. After these improvements of the BNN preconditioned conjugate gradient algorithm, we compare its performance against that of the BDDC preconditioners on a pair of large‐scale distributed‐memory platforms. The enhanced BNN method is a competitive preconditioner for three‐dimensional Poisson and elasticity problems and outperforms the BDDC method in many cases. Copyright © 2013 John Wiley & Sons, Ltd.
Bibliography:ark:/67375/WNG-93G7NPTJ-N
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ArticleID:NME4541
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SourceType-Scholarly Journals-1
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ISSN:0029-5981
1097-0207
DOI:10.1002/nme.4541