Previous |  Up |  Next

Article

Full entry | Fulltext not available (moving wall 24 months)      Feedback
Keywords:
two-level method; aggressive coarsening; smoothed aggregation; polynomial smoother; convergence analysis
Summary:
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.
References:
[1] Brandt, A.: 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] Brousek, J., Franková, P., Hanuš, M., Kopincová, H., Kužel, R., Tezaur, R., Vaněk, P., Vastl, Z.: 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] Ciarlet, P. G.: 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] Hackbusch, W.: 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] Tezaur, R., Vaněk, P.: 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] Toselli, A., Widlund, O.: 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] Vaněk, P., Brezina, M., Mandel, J.: Convergence of algebraic multigrid based on smoothed aggregation. Numer. Math. 88 (2001), 559-579. DOI 10.1007/s002110000226 | MR 1835471 | Zbl 0992.65139
[8] Vaněk, P., Brezina, M., Tezaur, R.: 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
Partner of
EuDML logo