On cyclic reduction and finite difference schemes
Journal of Computational and Applied Mathematics
Algebraic Multigrid for Linear Systems Obtained by Explicit Element Reduction
SIAM Journal on Scientific Computing
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We consider the use of the multigrid method in conjunction with a cyclic reduction preconditioner for convection-diffusion equations. This preconditioner corresponds to algebraically eliminating all the unknowns associated with the red points on a standard mesh colored in a checker-board fashion. It is shown that the multigrid method applied to the resulting operator often converges much faster than when applied to the original equations. Fourier analysis of a constant coefficient model problem as well as numerical results for nonconstant coefficient examples are used to validate the conclusions.