Numerical assessment of two-level domain decomposition preconditioners for incompressible Stokes and elasticity equations

Research output: Contribution to journalArticle

Abstract

Solving the linear elasticity and Stokes equations by an optimal domain decomposition method derived algebraically involves the use of non standard interface conditions. The one-level domain decomposition preconditioners are based on the solution of local problems. This has the undesired consequence that the results are not scalable, it means that the number of iterations needed to reach convergence increases with the number of subdomains. This is the reason why in this work we introduce, and test numerically, two-level preconditioners. Such preconditioners use a coarse space in their construction. We consider the nearly incompressible elasticity problems and Stokes equations, and discretise them by using two finite element methods, namely, the hybrid discontinuous Galerkin and Taylor-Hood discretisations.
LanguageEnglish
Pages41-63
Number of pages23
JournalETNA - Electronic Transactions on Numerical Analysis
Volume49
DOIs
Publication statusPublished - 20 Apr 2018

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Domain Decomposition
Stokes
Preconditioner
Elasticity
Stokes Equations
Optimal Domain
Interface Conditions
Elasticity Problem
Discontinuous Galerkin
Linear Elasticity
Domain Decomposition Method
Discretization
Finite Element Method
Iteration

Keywords

  • Stokes problem
  • nearly incompressible elasticity
  • Taylor-Hood
  • hybrid discontinuous Galerkin methods
  • domain decomposition
  • coarse space
  • optimized restricted additive Schwarz methods

Cite this

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title = "Numerical assessment of two-level domain decomposition preconditioners for incompressible Stokes and elasticity equations",
abstract = "Solving the linear elasticity and Stokes equations by an optimal domain decomposition method derived algebraically involves the use of non standard interface conditions. The one-level domain decomposition preconditioners are based on the solution of local problems. This has the undesired consequence that the results are not scalable, it means that the number of iterations needed to reach convergence increases with the number of subdomains. This is the reason why in this work we introduce, and test numerically, two-level preconditioners. Such preconditioners use a coarse space in their construction. We consider the nearly incompressible elasticity problems and Stokes equations, and discretise them by using two finite element methods, namely, the hybrid discontinuous Galerkin and Taylor-Hood discretisations.",
keywords = "Stokes problem, nearly incompressible elasticity, Taylor-Hood, hybrid discontinuous Galerkin methods, domain decomposition, coarse space, optimized restricted additive Schwarz methods",
author = "Barrenechea, {Gabriel R.} and Michał Bosy and Victorita Dolean",
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language = "English",
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journal = "ETNA - Electronic Transactions on Numerical Analysis",
issn = "1068-9613",
publisher = "Kent State University",

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AU - Barrenechea, Gabriel R.

AU - Bosy, Michał

AU - Dolean, Victorita

PY - 2018/4/20

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N2 - Solving the linear elasticity and Stokes equations by an optimal domain decomposition method derived algebraically involves the use of non standard interface conditions. The one-level domain decomposition preconditioners are based on the solution of local problems. This has the undesired consequence that the results are not scalable, it means that the number of iterations needed to reach convergence increases with the number of subdomains. This is the reason why in this work we introduce, and test numerically, two-level preconditioners. Such preconditioners use a coarse space in their construction. We consider the nearly incompressible elasticity problems and Stokes equations, and discretise them by using two finite element methods, namely, the hybrid discontinuous Galerkin and Taylor-Hood discretisations.

AB - Solving the linear elasticity and Stokes equations by an optimal domain decomposition method derived algebraically involves the use of non standard interface conditions. The one-level domain decomposition preconditioners are based on the solution of local problems. This has the undesired consequence that the results are not scalable, it means that the number of iterations needed to reach convergence increases with the number of subdomains. This is the reason why in this work we introduce, and test numerically, two-level preconditioners. Such preconditioners use a coarse space in their construction. We consider the nearly incompressible elasticity problems and Stokes equations, and discretise them by using two finite element methods, namely, the hybrid discontinuous Galerkin and Taylor-Hood discretisations.

KW - Stokes problem

KW - nearly incompressible elasticity

KW - Taylor-Hood

KW - hybrid discontinuous Galerkin methods

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KW - coarse space

KW - optimized restricted additive Schwarz methods

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