Abstract
In this study we demonstrate how some different techniques which were introduced and studied in previous works by the authors can be integrated and extended in the construction of efficient algebraic multilevel iteration methods for more complex problems. We devise an optimal order algorithm for solving linear systems obtained from locking-free discretization of 3D pure displacement elasticity problems. The presented numerical results illustrate the robustness of the method for nearly incompressible materials.
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References
Axelsson, O., Vassilevski, P.S.: Algebraic Multilevel Preconditioning Methods I. Numer. Math. 56, 157–177 (1989)
Axelsson, O., Vassilevski, P.S.: Algebraic Multilevel Preconditioning Methods II. SIAM J. Numer. Anal. 27, 1569–1590 (1990)
Blaheta, R., Margenov, S., Neytcheva, M.: Aggregation-based multilevel preconditioning of non-conforming FEM elasticity problems. In: Dongarra, J., Madsen, K., Waśniewski, J. (eds.) PARA 2004. LNCS, vol. 3732, pp. 847–856. Springer, Heidelberg (2004)
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 with Applications 11(4), 309–326 (2004)
Brenner, S., Scott, L.: The mathematical theory of finite element methods. Texts in applied mathematics, vol. 15. Springer, Heidelberg (1994)
Brenner, S., Sung, L.: Linear finite element methods for planar linear elasticity. Math. Comp. 59, 321–338 (1992)
Falk, R.S.: Nonconforming finite element methods for the equations of linear elasticity. Math. Comp. 57, 529–550 (1991)
Fortin, M., Glowinski, R.: Augmented Lagrangian methods: Applications to the numerical solution of boundary value problems, vol. 15. North-Holland Publishing Co., Amsterdam (1983)
Georgiev, I., Kraus, J., Margenov, S.: Multilevel algorithms for Rannacher-Turek finite element approximation of 3D elliptic problems. Computing 82, 217–239 (2008)
Kraus, J., Margenov, S.: Robust Algebraic Multilevel Methods and Algorithms. Radon Series Comp. Appl. Math. 5 (2009)
Kraus, J., Margenov, S., Synka, J.: On the multilevel preconditioning of Crouzeix-Raviart elliptic problems. Numer. Lin. Alg. Appl. 15, 395–416 (2008)
Lee, Y., Wu, J., Xu, J., Zikatanov, L.: Robust subspace correction methods for nearly singular systems. Mathematical Models and Methods in Applied Sciences 17(11), 1937–1963 (2007)
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Georgiev, I., Kraus, J., Margenov, S. (2010). Multilevel Preconditioning of Crouzeix-Raviart 3D Pure Displacement Elasticity Problems. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2009. Lecture Notes in Computer Science, vol 5910. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12535-5_10
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DOI: https://doi.org/10.1007/978-3-642-12535-5_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-12534-8
Online ISBN: 978-3-642-12535-5
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