Results of a theoretical analysis of the convergence of geometric multigrid algorithms in solving linear boundary value problems on two-block grids are presented. The smoothing property for a nonsymmetric iterative method with parameter and the convergence of the robust multigrid technique are proved. It is shown that the number of multigrid iterations does not depend on either the step size or the number of grid blocks. Results of computational experiments on solving a three-dimensional Dirichlet boundary value problem for a Poisson equation are given, which illustrate the theoretical analysis. This paper is of interest for developers of highly efficient algorithms to solve boundary value problems in domains with complicated geometry.
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