Geodesic
Multigrid method for elliptic equations with anisotropic discontinuous coefficients
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 7, pp. 1168-1182

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For difference elliptic equations, an algorithm based on Fedorenko’s multigrid method is constructed. The algorithm is intended for solving three-dimensional boundary value problems for equations with anisotropic discontinuous coefficients on parallel computers. Numerical results confirming the performance and parallel efficiency of the multigrid algorithm are presented. These qualities are ensured by using, as a multigrid triad, the standard Chebyshev iteration for coarsest grid equations, Chebyshev-type smoothing explicit iterative procedures, and intergrid transfer operators in problem-dependent form. 
@article{ZVMMF_2015_55_7_a6,
     author = {V. T. Zhukov and N. D. Novikova and O. B. Feodoritova},
     title = {Multigrid method for elliptic equations with anisotropic discontinuous coefficients},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1168--1182},
     publisher = {mathdoc},
     volume = {55},
     number = {7},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_7_a6/}
}
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V. T. Zhukov; N. D. Novikova; O. B. Feodoritova. Multigrid method for elliptic equations with anisotropic discontinuous coefficients. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 7, pp. 1168-1182. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_7_a6/