Applications of Mathematics, Vol. 63, No. 6, pp. 629-641, 2018


Improved convergence estimate for a multiply polynomially smoothed two-level method with an aggressive coarsening

Radek Tezaur, Petr Vaněk

Received November 13, 2017.   Published online November 23, 2018.

Abstract:  A variational two-level method in the class of methods with an aggressive coarsening and a massive polynomial smoothing is proposed. The method is a modification of the method of Section 5 of Tezaur, Vaněk (2018). Compared to that method, a significantly sharper estimate is proved while requiring only slightly more computational work.
Keywords:  two-level method; aggressive coarsening; smoothed aggregation; polynomial smoother; convergence analysis
Classification MSC:  65F10, 65M55


References:
[1] A. Brandt: Algebraic multigrid theory: The symmetric case. Appl. Math. Comput. 19 (1986), 23-56. DOI 10.1016/0096-3003(86)90095-0 | MR 0849831 | Zbl 0616.65037
[2] J. Brousek, P. Franková, M. Hanuš, H. Kopincová, R. Kužel, R. Tezaur, P. Vaněk, Z. Vastl: An overview of multilevel methods with aggressive coarsening and massive polynomial smoothing. ETNA, Electron. Trans. Numer. Anal. 44 (2015), 401-442. MR 3392685 | Zbl 1327.65058
[3] P. G. Ciarlet: The Finite Element Method for Elliptic Problems. Studies in Mathematics and Its Applications 4, North-Holland Publishing Company, Amsterdam (1978). DOI 10.1016/S0168-2024(08)70174-7 | MR 0520174 | Zbl 0383.65058
[4] W. Hackbusch: Multi-Grid Methods and Applications. Springer Series in Computational Mathematics 4, Springer, Berlin (1985). DOI 10.1007/978-3-662-02427-0 | MR 0814495 | Zbl 0595.65106
[5] R. Tezaur, P. Vaněk: Improved convergence bounds for two-level methods with an aggressive coarsening and massive polynomial smoothing. ETNA, Electron. Trans. Numer. Anal. 48 (2018), 264-285. DOI 10.1553/etna_vol48s264 | MR 3844102 | Zbl 06932099
[6] A. Toselli, O. Widlund: Domain Decomposition Methods - Algorithms and Theory. Springer Series in Computational Mathematics 34, Springer, Berlin (2005). DOI 10.1007/b137868 | MR 2104179 | Zbl 1069.65138
[7] P. Vaněk, M. Brezina, J. Mandel: Convergence of algebraic multigrid based on smoothed aggregation. Numer. Math. 88 (2001), 559-579. DOI 10.1007/s002110000226 | MR 1835471 | Zbl 0992.65139
[8] P. Vaněk, M. Brezina, R. Tezaur: Two-grid method for linear elasticity on unstructured meshes. SIAM J. Sci. Comput. 21 (1999), 900-923. DOI 10.1137/S1064827596297112 | MR 1755171 | Zbl 0952.65099

Affiliations:   Radek Tezaur, Department of Aeronautics and Astronautics, Stanford University, Durand Building, 496 Lomita Mall, Stanford, CA 94305, USA, e-mail: rtezaur@stanford.edu; Petr Vaněk, Department of Mathematics, University of West Bohemia, Univerzitní 22, 306 14 Plzeň, Czech Republic, e-mail: petrvanek09@seznam.cz


 
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