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Multigrid method for the plane problem of elasticity theory

Multigrid method for the plane problem of elasticity theory - A new approach to constructing multigrid methods for solving systems of linear algebraic equations is considered using the plane problem of elasticity theory as an example. This approach is based on the ideas of the domain decomposition method. Theoretical estimates are obtained for the rate of convergence of two- and three-grid methods, which are independent of the grid step size h. The results of numerical experiments are given, and they are compared with the theoretical estimates. Multigrid methods first suggested and investigated in [1,5,6] and then actively developed in the last decade [2,7,10,11] are referred to the most efficient iterative methods for solving systems of grid equations. In this paper, using the results of [8] we suggest a new approach to constructing multigrid methods for solving systems of linear algebraic equations arising as a result of the finite element approximation of the plane problem of elasticity theory. In Section 1, we formulate the original problem and construct the finite element method in whose terms it is reduced to an algebraic system. In Section 2, we construct grids used henceforth and define the functionals required. In Sections 3 and 4, we consequently consider two- and three-grid domain decomposition http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Russian Journal of Numerical Analysis and Mathematical Modelling de Gruyter

Multigrid method for the plane problem of elasticity theory

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Publisher
de Gruyter
Copyright
Copyright © 2009 Walter de Gruyter
ISSN
0927-6467
eISSN
1569-3988
DOI
10.1515/rnam.1990.5.2.137
Publisher site
See Article on Publisher Site

Abstract

- A new approach to constructing multigrid methods for solving systems of linear algebraic equations is considered using the plane problem of elasticity theory as an example. This approach is based on the ideas of the domain decomposition method. Theoretical estimates are obtained for the rate of convergence of two- and three-grid methods, which are independent of the grid step size h. The results of numerical experiments are given, and they are compared with the theoretical estimates. Multigrid methods first suggested and investigated in [1,5,6] and then actively developed in the last decade [2,7,10,11] are referred to the most efficient iterative methods for solving systems of grid equations. In this paper, using the results of [8] we suggest a new approach to constructing multigrid methods for solving systems of linear algebraic equations arising as a result of the finite element approximation of the plane problem of elasticity theory. In Section 1, we formulate the original problem and construct the finite element method in whose terms it is reduced to an algebraic system. In Section 2, we construct grids used henceforth and define the functionals required. In Sections 3 and 4, we consequently consider two- and three-grid domain decomposition

Journal

Russian Journal of Numerical Analysis and Mathematical Modellingde Gruyter

Published: Jan 1, 1990

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