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

Barrenechea, GR; Bosy, M; Dolean, V; (2018) Numerical assessment of two-level domain decomposition preconditioners for incompressible Stokes and elasticity equations. Electronic Transactions on Numerical Analysis (ETNA) , 49 pp. 41-63. 10.1553/etna_vol49s41. Green open access

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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, which 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.

Type: Article
Title: Numerical assessment of two-level domain decomposition preconditioners for incompressible Stokes and elasticity equations
Open access status: An open access version is available from UCL Discovery
DOI: 10.1553/etna_vol49s41
Publisher version: https://doi.org/10.1553/etna_vol49s41
Language: English
Additional information: This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Stokes problem, nearly incompressible elasticity, Taylor-Hood, hybrid discontinuous Galerkin methods, domain decomposition, coarse space, optimized restricted additive Schwarz methods
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
URI: https://discovery.ucl.ac.uk/id/eprint/10080990
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