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Abstract
We study the behavior of the CBS constant as a quality measure for hierarchical two-level splittings of quadratic FEM stiffness matrices. The article is written in the spirit of [3] where the focus is on the robustness with respect to mesh and coefficient anisotropy. The considered splittings are: Differences and Aggregates (DA); First Reduce (FR); and hierarchical P-decomposition (P). The presented results show sufficient conditions for the existence of optimal order Algebraic MultiLevel Iteration (AMLI) preconditioners.
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References
Axelsson, O.: Stabilization of Algebraic Multilevel Iteration method; additive methods. Numerical Algorithms, 23–47 (1999)
Blaheta, R., Margenov, S., Neytcheva, M.: Uniform Estimate of the Constant in the Strengthened CBS inequality for Anisotropic Non-conforming FEM systems. Numerical Linear Algebra and Applications 11(4), 309–326 (2004)
Kraus, J., Margenov, S.: Robust Algebraic Multilevel Methods and Algorithms. De Gruyter, Germany (2009)
Maitre, J.F., Musy, S.: The Contraction Number of a Class of Two-level Methods; An Exact Evaluation for Some Finite Element Subspaces and Model Problems. Lect. Notes Math., vol. 960, pp. 535–544 (1982)
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Authors and Affiliations
Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 8, 1113, Sofia, Bulgaria
Ivan Georgiev
Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 25A, 1113, Sofia, Bulgaria
Maria Lymbery & Svetozar Margenov
- Ivan Georgiev
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- Maria Lymbery
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- Svetozar Margenov
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Editors and Affiliations
Institute of Computer and Communication Technologies, Bulgarian Academy of Sciences, Acad. G. Bonchev 25 A, 1113, Sofia, Bulgaria
Ivan Dimov
Faculty of Mathematics and Informatics, Department Numerical Methods and Algorithms, University of Sofia "St. Kliment Ohridski",, blvd. James Bourchier 5, 1164, Sofia, Bulgaria
Stefka Dimova
Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. Bonchev St.,Bl.8, 1113, Sofia, Bulgaria
Natalia Kolkovska
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Georgiev, I., Lymbery, M., Margenov, S. (2011). Analysis of the CBS Constant for Quadratic Finite Elements. In: Dimov, I., Dimova, S., Kolkovska, N. (eds) Numerical Methods and Applications. NMA 2010. Lecture Notes in Computer Science, vol 6046. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18466-6_49
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