Geodesic
Application of robust multigrid technique for parallel solution of the initial-boundary problems
Matematičeskoe modelirovanie, Tome 34 (2022) no. 5, pp. 73-87

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The article is devoted to development of a parallel multigrid algorithm for numerical solution of (non)linear initial-boundary value problems (implicit schemes) based on the Robust Multigrid Technique (RMT). Advantage of the proposed algorithm is opportunity of parallel solution of boundary value problems and initial-boundary value problems in unified manner using $m=1,2,3,\dots$ independent computers (threads, if parallelization technology OpenMP used). Coarse grids are generated only in space, the number of grid levels depends on the coefficient matrix condition number of the resulting system of linear algebraic equations. Point Gauss-Seidel method is used as a smoothing procedure for solving the initial-boundary value problem for the heat conductivity equation. Description of the algorithm and results of computational experiments performed using the OpenMP technology are given.
Keywords: initial boundary value problems, parallel computing, multigrid methods. 
@article{MM_2022_34_5_a4,
     author = {S. I. Martynenko and I. G\"okalp and V. A. Bakhtin and M. Karaca and P. D. Toktaliev and P. A. Semenev},
     title = {Application of robust multigrid technique for parallel solution of the initial-boundary problems},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {73--87},
     publisher = {mathdoc},
     volume = {34},
     number = {5},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2022_34_5_a4/}
}
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S. I. Martynenko; I. Gökalp; V. A. Bakhtin; M. Karaca; P. D. Toktaliev; P. A. Semenev. Application of robust multigrid technique for parallel solution of the initial-boundary problems. Matematičeskoe modelirovanie, Tome 34 (2022) no. 5, pp. 73-87. http://geodesic.mathdoc.fr/item/MM_2022_34_5_a4/