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Keywords:
aggregation class; two-level algorithm; convergence factor; smoothing operator; linear algebraic system
aggregation class; two-level algorithm; convergence factor; smoothing operator; linear algebraic system
Summary:
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.
References:
[1] Blaheta R.: Iteration methods for numerical solution of boundary elasticity problems. VÚB, Ostrava, 1987, Dissertation. (In Czech.)
[2] Blaheta R.: A multi-level method with correction by aggregation for solving discrete elliptic problems. Aplikace matematiky 5 no. 31 (1986), 365-378. MR 0863032 | Zbl 0615.65103
[3] Brandt A.: Algebraic Multigrid Theory: The Symmetric Case. Preliminary Proceedings of the International Multigrid Conference, Copper Mountain, Colorado, April 6-8 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. MR 0972752
[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.
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