| Title:
|
Improved convergence estimate for a multiply polynomially smoothed two-level method with an aggressive coarsening (English) |
| Author:
|
Tezaur, Radek |
| Author:
|
Vaněk, Petr |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
63 |
| Issue:
|
6 |
| Year:
|
2018 |
| Pages:
|
629-641 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
two-level method |
| Keyword:
|
aggressive coarsening |
| Keyword:
|
smoothed aggregation |
| Keyword:
|
polynomial smoother |
| Keyword:
|
convergence analysis |
| MSC:
|
65F10 |
| MSC:
|
65M55 |
| idZBL:
|
Zbl 07031680 |
| idMR:
|
MR3893003 |
| DOI:
|
10.21136/AM.2018.0314-17 |
| . |
| Date available:
|
2019-01-03T09:09:46Z |
| Last updated:
|
2021-01-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147561 |
| . |
| Reference:
|
[1] Brandt, A.: Algebraic multigrid theory: The symmetric case.Appl. Math. Comput. 19 (1986), 23-56. Zbl 0616.65037, MR 0849831, 10.1016/0096-3003(86)90095-0 |
| Reference:
|
[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. Zbl 1327.65058, MR 3392685 |
| Reference:
|
[3] Ciarlet, P. G.: The Finite Element Method for Elliptic Problems.Studies in Mathematics and Its Applications 4, North-Holland Publishing Company, Amsterdam (1978). Zbl 0383.65058, MR 0520174, 10.1016/S0168-2024(08)70174-7 |
| Reference:
|
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| Reference:
|
[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. Zbl 06932099, MR 3844102, 10.1553/etna_vol48s264 |
| Reference:
|
[6] Toselli, A., Widlund, O.: Domain Decomposition Methods---Algorithms and Theory.Springer Series in Computational Mathematics 34, Springer, Berlin (2005). Zbl 1069.65138, MR 2104179, 10.1007/b137868 |
| Reference:
|
[7] Vaněk, P., Brezina, M., Mandel, J.: Convergence of algebraic multigrid based on smoothed aggregation.Numer. Math. 88 (2001), 559-579. Zbl 0992.65139, MR 1835471, 10.1007/s002110000226 |
| Reference:
|
[8] Vaněk, P., Brezina, M., Tezaur, R.: Two-grid method for linear elasticity on unstructured meshes.SIAM J. Sci. Comput. 21 (1999), 900-923. Zbl 0952.65099, MR 1755171, 10.1137/S1064827596297112 |
| . |
