On Multigrid Methods for Solving Two-Dimensional Boundary-Value Problems

Y. L. Gurieva, V. P. Il’in, A. V. Petukhov

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)118-127
Number of pages10
JournalJournal of Mathematical Sciences (United States)
Issue number2
Publication statusPublished - 1 Aug 2020

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