Geodesic
Multigrid methods for solving two-dimensional boundary-value problems
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXII, Tome 482 (2019), pp. 13-27

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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 the approximate Schur complement obtained by eliminating the edge nodes of the coarse grid are described on an 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. 
@article{ZNSL_2019_482_a1,
     author = {Ya. L. Gurieva and V. P. Il'in and A. V. Petukhov},
     title = {Multigrid methods for solving two-dimensional boundary-value problems},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {13--27},
     publisher = {mathdoc},
     volume = {482},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_482_a1/}
}
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Ya. L. Gurieva; V. P. Il'in; A. V. Petukhov. Multigrid methods for solving two-dimensional boundary-value problems. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXII, Tome 482 (2019), pp. 13-27. http://geodesic.mathdoc.fr/item/ZNSL_2019_482_a1/