Model analysis of BPX preconditioner based on smoothed aggregation

Pavla Fraňková; Jan Mandel; Petr Vaněk

Applications of Mathematics (2015)

  • Volume: 60, Issue: 3, page 219-250
  • ISSN: 0862-7940

Abstract

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We prove nearly uniform convergence bounds for the BPX preconditioner based on smoothed aggregation under the assumption that the mesh is regular. The analysis is based on the fact that under the assumption of regular geometry, the coarse-space basis functions form a system of macroelements. This property tends to be satisfied by the smoothed aggregation bases formed for unstructured meshes.

How to cite

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Fraňková, Pavla, Mandel, Jan, and Vaněk, Petr. "Model analysis of BPX preconditioner based on smoothed aggregation." Applications of Mathematics 60.3 (2015): 219-250. <http://eudml.org/doc/270083>.

@article{Fraňková2015,
abstract = {We prove nearly uniform convergence bounds for the BPX preconditioner based on smoothed aggregation under the assumption that the mesh is regular. The analysis is based on the fact that under the assumption of regular geometry, the coarse-space basis functions form a system of macroelements. This property tends to be satisfied by the smoothed aggregation bases formed for unstructured meshes.},
author = {Fraňková, Pavla, Mandel, Jan, Vaněk, Petr},
journal = {Applications of Mathematics},
keywords = {smoothed aggregation; parallel preconditioner; BPX preconditioner; smoothed aggregation; parallel preconditioner; BPX preconditioner},
language = {eng},
number = {3},
pages = {219-250},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Model analysis of BPX preconditioner based on smoothed aggregation},
url = {http://eudml.org/doc/270083},
volume = {60},
year = {2015},
}

TY - JOUR
AU - Fraňková, Pavla
AU - Mandel, Jan
AU - Vaněk, Petr
TI - Model analysis of BPX preconditioner based on smoothed aggregation
JO - Applications of Mathematics
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 3
SP - 219
EP - 250
AB - We prove nearly uniform convergence bounds for the BPX preconditioner based on smoothed aggregation under the assumption that the mesh is regular. The analysis is based on the fact that under the assumption of regular geometry, the coarse-space basis functions form a system of macroelements. This property tends to be satisfied by the smoothed aggregation bases formed for unstructured meshes.
LA - eng
KW - smoothed aggregation; parallel preconditioner; BPX preconditioner; smoothed aggregation; parallel preconditioner; BPX preconditioner
UR - http://eudml.org/doc/270083
ER -

References

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  2. Bramble, J. H., Pasciak, J. E., Xu, J., 10.1090/S0025-5718-1990-1023042-6, Math. Comput. 55 (1990), 1-22. (1990) Zbl0725.65095MR1023042DOI10.1090/S0025-5718-1990-1023042-6
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  5. Vaněk, P., Fast multigrid solver, Appl. Math., Praha 40 1-20 (1995). (1995) Zbl0824.65016MR1305645
  6. Vaněk, P., Brezina, M., 10.1007/s10492-013-0018-2, Appl. Math., Praha 58 369-388 (2013). (2013) Zbl1289.65064MR3083519DOI10.1007/s10492-013-0018-2
  7. Vaněk, P., Brezina, M., Mandel, J., 10.1007/s211-001-8015-y, Numer. Math. 88 559-579 (2001). (2001) Zbl0992.65139MR1835471DOI10.1007/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, M., 10.1007/BF02238511, Computing 56 (1996), 179-196. (1996) MR1393006DOI10.1007/BF02238511
  10. Vaněk, P., Mandel, J., Brezina, M., Algebraic multigrid on unstructured meshes, UCD/CCM Report 34, Center for Computational Mathematics, University of Colorado at Denver, http://www.math.cudenver.edu/ccmreports/rep34.ps.gz, 1994. 

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