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Using a compensation principle in the algebraic multilevel iteration method for finite element matrices. (English. Russian summary) Zbl 1079.65030
An improved version is proposed of the algebraic multilevel iteration method for finite element matrices, which was offered by O.  Axelsson and M.  Larin [J. Comput. Appl. Math. 89, No. 1, 135–153 (1998; Zbl 0941.65036)]. To speed up the rate of convergence, a family of iterative parameters is used, which are chosen on the base of an error compensation principle. Results of numerical experiments on standard test problems are presented.
MSC:
65F10 Iterative numerical methods for linear systems
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65Y20 Complexity and performance of numerical algorithms
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65F35 Numerical computation of matrix norms, conditioning, scaling
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