Estimate for the Arithmetical Cost of an Algebraic Multigrid Preconditioner
Abstract
A multigrid preconditioner for the matrix arising in finite element approximation of model elliptic boundary value problem is proposed. Hierarchical triangular grids with bisection form the basis of multigrid construction. The main purpose of the paper is to evaluate the arithmetical cost of a preconditioner step.
References
Yu.A. Kuznetsov, “Algebraic multigrid domain decomposition methods”, Sov. J. Numer. Anal. Math. Modelling, vol.4, No.5, pp. 351-379, 1989.
Yu.R. Hakopian and Yu.A. Kuznetsov, “Algebraic multigrid/substructuring preconditioners on triangular grids”, Sov. J. Numer. Anal. Math. Modelling, vol.6, No.6, pp. 453-483, 1991.
O. Axelsson, Yu.R. Hakopian and Yu.A. Kuznetsov, “Multilevel preconditioning for perturbed finite element matrices”, IMA J. Numer. Anal., vol.17, pp. 125-149, 1997.
Yu.R. Hakopian, “Algebraic multilevel/substructuring preconditioner in finite element method with piecewise quadratic approximation”, “Mathematical Problems of Computer Science”, vol.21, pp. 164-180, 2000.
Yu.R. Hakopian, “Algebraic multilevel preconditioners for third order finite element approximation”, Algebra, Geometry & their Applications (Seminar Proceedings), Yerevan State University, Armenia, vol.1, pp. 20-39, 2001.
Yu.R. Hakopian and A.S. Harutyunyan, “Two-level preconditioners for serendipity finite element matrices”, Linear Algebra Appl., vol.13, No.10, pp. 847-864, 2006.
G. Strang and G. Fix, “An Analysis of the Finite Element Method”, Prentice-Hall Englewood Cliffs, N.J., 1973.
O.C. Zenkiewich and K. Morgan, “Finite Elements and Approximation”, Wiley, NY, 1983.
O. Axelsson and P.S.Vassilevski, “Algebraic multilevel preconditioning methods”, I, Numer. Math., vol. 56, pp. 157-177, 1989.
O. Axelsson. Iterative Solution Methods, Cambridge University Press, 1994.
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