Multigrid methods with skew-Hermitian based smoothers for the convection–diffusion problem with dominant convection




convection-diffusion equation, multigrid methods, smoothing procedure, product-type skew-Hermitian triangular splitting, local Fourier analysis, convergence


The convection–diffusion equation with dominant convection is considered on a uniform grid of central difference scheme. The multigrid method is used for solving the strongly nonsymmetric systems of linear algebraic equations with positive definite coefficient matrices. Two-step skew-Hermitian iterative methods are utilized for the first time as a smoothing procedure. It is demonstrated that using the proper smoothers enables to improve the convergence of the multigrid method. The robustness of the smoothers with respect to variation of the Peclet number is shown by local Fourier analysis and numerical experiments.

Author Biographies

Tatiana S. Martynova

Southern Federal University,
Vorovich Institute for Mathematics, Mechanics and Computer Science,
• Senior Researcher

Galina V. Muratova

Southern Federal University,
Vorovich Institute for Mathematics, Mechanics and Computer Science,
• Professor

Irina N. Shabas

Southern Federal University,
Vorovich Institute for Mathematics, Mechanics and Computer Science,
• Senior Researcher

Vadim V. Bavin

Southern Federal University,
Vorovich Institute for Mathematics, Mechanics and Computer Science,
• Junior Researcher


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How to Cite

Martynova Tatiana S., Muratova Galina V., Shabas Irina N., Bavin Vadim V. Multigrid Methods With Skew-Hermitian Based Smoothers for the convection–diffusion Problem With Dominant Convection // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2022. 23. 46-59. doi 10.26089/NumMet.v23r104



Methods and algorithms of computational mathematics and their applications