Gabriel R. Barrenechea,
Michał Bosy,
Victorita Dolean
S. 41 - 63
doi:
10.1553/etna_vol49s41
Verlag der Österreichischen Akademie der Wissenschaften
doi:
10.1553/etna_vol49s41
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.
Stokes problem, nearly incompressible elasticity, Taylor-Hood, hybrid discontinuous Galerkin methods, domain decomposition, coarse space, optimized restricted additive Schwarz methods
Published Online:
2018/04/19 10:01:33
Document Date:
2018/04/19 09:27:00
Object Identifier:
0xc1aa5576 0x003892f2
Rights:All rights reserved.For questions regarding copyright and copies please contact us by email.
Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613.
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