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An efficient multiscale‐like multigrid computation for 2D convection‐diffusion equations on nonuniform grids
Author(s) -
Li Ming,
Zheng Zhoushun
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6895
Subject(s) - multigrid method , discretization , mathematics , interpolation (computer graphics) , computation , convection–diffusion equation , grid , mathematical optimization , mathematical analysis , partial differential equation , algorithm , geometry , computer science , animation , computer graphics (images)
An efficient multiscale‐like multigrid (MSLMG) method combined with a high‐order compact (HOC) difference scheme on nonuniform grids is presented to solve the two‐dimensional (2D) convection‐diffusion equations. The discrete systems with given appropriate initial solutions on two finest grids are solved to obtain the MSLMG solutions with discretization‐level accuracy by performing fewer multigrid cycles; it is implemented with alternating line Gauss–Seidel smoother, interpolation, and restriction operators on the nonuniform grids. Numerical experiments of boundary layer or local singularity problems are conducted to show that the proposed algorithm with the HOC scheme on nonuniform grids is efficient and effective to decrease the computational cost and time, and the computed approximation on the nonuniform grids has fourth order accuracy.