Abstract
Various methods for constructing algebraic multigrid type methods for solving multidimensional boundary-value problems are considered. Two-level iterative algorithms in Krylov subspaces based on approximating the Schur complement obtained by eliminating the edge nodes of the coarse grid are described on the example of two-dimensional rectangular grids. Some aspects of extending the methods proposed to the multilevel case, to nested triangular grids, and also to three-dimensional grids are discussed. A comparison with the classical multigrid methods based on using smoothing, restriction (aggregation), coarse-grid correction, and prolongation is provided. The efficiency of the algorithms suggested is demonstrated by numerical results for some model problems.
Original language | English |
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Pages (from-to) | 118-127 |
Number of pages | 10 |
Journal | Journal of Mathematical Sciences (United States) |
Volume | 249 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1 Aug 2020 |