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Numerical methods and programming, 2000, Volume 1, Issue 1, Pages 83–102
(Mi vmp809)
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This article is cited in 4 scientific papers (total in 4 papers)
Robust multigrid technique for solving partial differential equations on structured grids
S. I. Martynenko Central Institute of Aviation Motors, State Scientific Center of Russian Federation, Moscow
Abstract:
A new robust multigrid technique for solving elliptic partial differential
equations is proposed. The technique is based on a united computational
algorithm that consists of the following stages: 1) adaption of equations to
numerical methods, 2) the control volume discretization, and 3) applying
multigrid iterations. Special subgrids of the finest grid are generated to
obtain the most powerful coarse grid correction strategy. Accuracy of the
transfer operators is independent of the mesh size on coarse grids; therefore,
a smoothing procedure and a multigrid cycle may be very simple. Expanded
robustness of the multigrid technique is a result of adaption of equations,
extremely accurate formulation of the discrete problems on the coarse grids,
original coarsening, the most powerful coarse grid correction strategy,
construction of problem-independent transfer operators, and absence of
pre-smoothing and interpolation. The paper represents the algorithm, estimates
of computational work, and results of numerical tests performed. Our numerical
tests demonstrate robustness and efficiency of our multigrid technique.
Keywords:
elliptic differential equations, multigrid iterations, multigrid methods, Navier-Stockes equations, finite-difference methods.
Citation:
S. I. Martynenko, “Robust multigrid technique for solving partial differential equations on structured grids”, Num. Meth. Prog., 1:1 (2000), 83–102
Linking options:
https://www.mathnet.ru/eng/vmp809 https://www.mathnet.ru/eng/vmp/v1/i1/p83
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Abstract page: | 131 | Full-text PDF : | 91 |
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