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...

Celý popis

Uložené v:

Podrobná bibliografia
Vydané v:	International journal for numerical methods in engineering Ročník 96; číslo 4; s. 203 - 230
Hlavní autori:	Badia, Santiago, Martín, Alberto F., Príncipe, Javier
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Chichester Blackwell Publishing Ltd 26.10.2013 Wiley Wiley Subscription Services, Inc
Predmet:	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
On-line prístup:	Získať plný text
Tagy:	Pridať tag Žiadne tagy, Buďte prvý, kto otaguje tento záznam!

Popis
Shrnutí:	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.
Bibliografia:	ark:/67375/WNG-93G7NPTJ-N istex:8370123F787924AE62DD7CE62BB02DEC5171897F ArticleID:NME4541 ObjectType-Article-1 SourceType-Scholarly Journals-1 content type line 14 ObjectType-Feature-2 content type line 23
ISSN:	0029-5981 1097-0207
DOI:	10.1002/nme.4541