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

Radek Tezaur; Petr Vaněk

Applications of Mathematics (2018)

  • Volume: 63, Issue: 6, page 629-641
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Tezaur, Radek, and Vaněk, Petr. "Improved convergence estimate for a multiply polynomially smoothed two-level method with an aggressive coarsening." Applications of Mathematics 63.6 (2018): 629-641. <http://eudml.org/doc/294278>.

@article{Tezaur2018,
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.},
author = {Tezaur, Radek, Vaněk, Petr},
journal = {Applications of Mathematics},
keywords = {two-level method; aggressive coarsening; smoothed aggregation; polynomial smoother; convergence analysis},
language = {eng},
number = {6},
pages = {629-641},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Improved convergence estimate for a multiply polynomially smoothed two-level method with an aggressive coarsening},
url = {http://eudml.org/doc/294278},
volume = {63},
year = {2018},
}

TY - JOUR
AU - Tezaur, Radek
AU - Vaněk, Petr
TI - Improved convergence estimate for a multiply polynomially smoothed two-level method with an aggressive coarsening
JO - Applications of Mathematics
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 6
SP - 629
EP - 641
AB - 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.
LA - eng
KW - two-level method; aggressive coarsening; smoothed aggregation; polynomial smoother; convergence analysis
UR - http://eudml.org/doc/294278
ER -

References

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  1. Brandt, A., 10.1016/0096-3003(86)90095-0, Appl. Math. Comput. 19 (1986), 23-56. (1986) Zbl0616.65037MR0849831DOI10.1016/0096-3003(86)90095-0
  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. (2015) Zbl1327.65058MR3392685
  3. Ciarlet, P. G., 10.1016/S0168-2024(08)70174-7, Studies in Mathematics and Its Applications 4, North-Holland Publishing Company, Amsterdam (1978). (1978) Zbl0383.65058MR0520174DOI10.1016/S0168-2024(08)70174-7
  4. Hackbusch, W., 10.1007/978-3-662-02427-0, Springer Series in Computational Mathematics 4, Springer, Berlin (1985). (1985) Zbl0595.65106MR0814495DOI10.1007/978-3-662-02427-0
  5. Tezaur, R., Vaněk, P., 10.1553/etna_vol48s264, ETNA, Electron. Trans. Numer. Anal. 48 (2018), 264-285. (2018) Zbl06932099MR3844102DOI10.1553/etna_vol48s264
  6. Toselli, A., Widlund, O., 10.1007/b137868, Springer Series in Computational Mathematics 34, Springer, Berlin (2005). (2005) Zbl1069.65138MR2104179DOI10.1007/b137868
  7. Vaněk, P., Brezina, M., Mandel, J., 10.1007/s002110000226, Numer. Math. 88 (2001), 559-579. (2001) Zbl0992.65139MR1835471DOI10.1007/s002110000226
  8. Vaněk, P., Brezina, M., Tezaur, R., 10.1137/S1064827596297112, SIAM J. Sci. Comput. 21 (1999), 900-923. (1999) Zbl0952.65099MR1755171DOI10.1137/S1064827596297112

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