Improved convergence bounds for smoothed aggregation method: linear dependence of the convergence rate on the number of levels

Jan Brousek; Pavla Fraňková; Petr Vaněk

Czechoslovak Mathematical Journal (2016)

  • Volume: 66, Issue: 3, page 829-845
  • ISSN: 0011-4642

Abstract

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The smoothed aggregation method has became a widely used tool for solving the linear systems arising by the discretization of elliptic partial differential equations and their singular perturbations. The smoothed aggregation method is an algebraic multigrid technique where the prolongators are constructed in two steps. First, the tentative prolongator is constructed by the aggregation (or, the generalized aggregation) method. Then, the range of the tentative prolongator is smoothed by a sparse linear prolongator smoother. The tentative prolongator is responsible for the approximation, while the prolongator smoother enforces the smoothness of the coarse-level basis functions.

How to cite

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Brousek, Jan, Fraňková, Pavla, and Vaněk, Petr. "Improved convergence bounds for smoothed aggregation method: linear dependence of the convergence rate on the number of levels." Czechoslovak Mathematical Journal 66.3 (2016): 829-845. <http://eudml.org/doc/286844>.

@article{Brousek2016,
abstract = {The smoothed aggregation method has became a widely used tool for solving the linear systems arising by the discretization of elliptic partial differential equations and their singular perturbations. The smoothed aggregation method is an algebraic multigrid technique where the prolongators are constructed in two steps. First, the tentative prolongator is constructed by the aggregation (or, the generalized aggregation) method. Then, the range of the tentative prolongator is smoothed by a sparse linear prolongator smoother. The tentative prolongator is responsible for the approximation, while the prolongator smoother enforces the smoothness of the coarse-level basis functions.},
author = {Brousek, Jan, Fraňková, Pavla, Vaněk, Petr},
journal = {Czechoslovak Mathematical Journal},
keywords = {smoothed aggregation; improved convergence bound},
language = {eng},
number = {3},
pages = {829-845},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Improved convergence bounds for smoothed aggregation method: linear dependence of the convergence rate on the number of levels},
url = {http://eudml.org/doc/286844},
volume = {66},
year = {2016},
}

TY - JOUR
AU - Brousek, Jan
AU - Fraňková, Pavla
AU - Vaněk, Petr
TI - Improved convergence bounds for smoothed aggregation method: linear dependence of the convergence rate on the number of levels
JO - Czechoslovak Mathematical Journal
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 3
SP - 829
EP - 845
AB - The smoothed aggregation method has became a widely used tool for solving the linear systems arising by the discretization of elliptic partial differential equations and their singular perturbations. The smoothed aggregation method is an algebraic multigrid technique where the prolongators are constructed in two steps. First, the tentative prolongator is constructed by the aggregation (or, the generalized aggregation) method. Then, the range of the tentative prolongator is smoothed by a sparse linear prolongator smoother. The tentative prolongator is responsible for the approximation, while the prolongator smoother enforces the smoothness of the coarse-level basis functions.
LA - eng
KW - smoothed aggregation; improved convergence bound
UR - http://eudml.org/doc/286844
ER -

References

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  3. Fraňková, P., Mandel, J., Vaněk, P., 10.1007/s10492-015-0093-7, Appl. Math., Praha 60 (2015), 219-250. (2015) MR3419960DOI10.1007/s10492-015-0093-7
  4. Vaněk, P., Fast multigrid solver, Appl. Math., Praha 40 (1995), 1-20. (1995) Zbl0824.65016MR1305645
  5. Vaněk, P., Acceleration of convergence of a two-level algorithm by smoothing transfer operator, Appl. Math., Praha 37 (1992), 265-274. (1992) MR1180605
  6. Vaněk, P., Brezina, M., 10.1007/s10492-013-0018-2, Appl. Math., Praha 58 (2013), 369-388. (2013) Zbl1289.65064MR3083519DOI10.1007/s10492-013-0018-2
  7. Vaněk, P., Brezina, M., Mandel, J., 10.1007/s211-001-8015-y, Numer. Math. 88 (2001), 559-579. (2001) MR1835471DOI10.1007/s211-001-8015-y
  8. Vaněk, P., Brezina, M., Tezaur, R., 10.1137/S1064827596297112, SIAM J. Sci Comput. 21 (1999), 900-923. (1999) MR1755171DOI10.1137/S1064827596297112
  9. Vaněk, P., Mandel, J., Brezina, R., 10.1007/BF02238511, Computing 56 (1996), 179-196. (1996) MR1393006DOI10.1007/BF02238511

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