Acceleration of convergence of a two-level algebraic algorithm by aggregation in smoothing process

Stanislav Míka; Petr Vaněk

Applications of Mathematics (1992)

  • Volume: 37, Issue: 5, page 343-356
  • ISSN: 0862-7940

Abstract

top
A two-level algebraic algorithm is introduced and its convergence is proved. The restriction as well as prolongation operators are defined with the help of aggregation classes. Moreover, a particular smoothing operator is defined in an analogical way to accelarate the convergence of the algorithm. A model example is presented in conclusion.

How to cite

top

Míka, Stanislav, and Vaněk, Petr. "Acceleration of convergence of a two-level algebraic algorithm by aggregation in smoothing process." Applications of Mathematics 37.5 (1992): 343-356. <http://eudml.org/doc/15720>.

@article{Míka1992,
abstract = {A two-level algebraic algorithm is introduced and its convergence is proved. The restriction as well as prolongation operators are defined with the help of aggregation classes. Moreover, a particular smoothing operator is defined in an analogical way to accelarate the convergence of the algorithm. A model example is presented in conclusion.},
author = {Míka, Stanislav, Vaněk, Petr},
journal = {Applications of Mathematics},
keywords = {aggregation class; two-level algorithm; convergence factor; smoothing operator; linear algebraic system; convergence acceleration; two-level algebraic algorithm; convergence; aggregation classes; smoothing operator},
language = {eng},
number = {5},
pages = {343-356},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Acceleration of convergence of a two-level algebraic algorithm by aggregation in smoothing process},
url = {http://eudml.org/doc/15720},
volume = {37},
year = {1992},
}

TY - JOUR
AU - Míka, Stanislav
AU - Vaněk, Petr
TI - Acceleration of convergence of a two-level algebraic algorithm by aggregation in smoothing process
JO - Applications of Mathematics
PY - 1992
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 37
IS - 5
SP - 343
EP - 356
AB - A two-level algebraic algorithm is introduced and its convergence is proved. The restriction as well as prolongation operators are defined with the help of aggregation classes. Moreover, a particular smoothing operator is defined in an analogical way to accelarate the convergence of the algorithm. A model example is presented in conclusion.
LA - eng
KW - aggregation class; two-level algorithm; convergence factor; smoothing operator; linear algebraic system; convergence acceleration; two-level algebraic algorithm; convergence; aggregation classes; smoothing operator
UR - http://eudml.org/doc/15720
ER -

References

top
  1. Blaheta R., Iteration methods for numerical solution of boundary elasticity problems, VÚB, Ostrava, 1987, Dissertation. (In Czech.) (1987) 
  2. Blaheta R., A multi-level method with correction by aggregation for solving discrete elliptic problems, Aplikace matematiky 5 no. 31 (1986), 365-378. (1986) Zbl0615.65103MR0863032
  3. Brandt A., Algebraic Multigrid Theory: The Symmetric Case, Preliminary Proceedings of the International Multigrid Conference, Copper Mountain, Colorado, April 6-8 1983. (1983) 
  4. Ruge J. W., Stüben K., Algebraic Multigrid, in [5]. 
  5. Multigrid Methods. Frontiers in Applied Mathematics, (Mc Cormick, S. F., ed.), Society for industrial and applied mathematics, Philadelphia, Pennsylvania, 1987. (1987) MR0972752
  6. Míka S., Vaněk P., On the convergence of a two-level algebraic algorithm, Sborník referátů VIII. letní školy Software a algoritmy numerické matematiky (Sušice 1989), JČMF, 1990. (1989) 

NotesEmbed ?

top

You must be logged in to post comments.