Fourier analysis of a robust multigrid method
for convection-diffusion equations |
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Authors: | Arnold Reusken |
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Institution: | (1) Department of Mathematics and Computing Science, Eindhoven, University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands , NL |
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Abstract: | Summary.
We consider a two-grid method for solving 2D convection-diffusion
problems. The coarse grid correction is based on approximation of
the Schur complement. As a preconditioner of the Schur complement we use the
exact Schur complement of modified fine grid equations. We assume constant
coefficients and periodic boundary conditions and apply Fourier analysis. We
prove an upper bound for the spectral radius of the two-grid iteration
matrix that is smaller than one and independent of the mesh size, the
convection/diffusion ratio and the flow direction; i.e. we have a (strong)
robustness result. Numerical results illustrating the robustness of the
corresponding multigrid -cycle are given.
Received October 14, 1994 |
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Keywords: | Mathematics Subject Classification (1991): 65N20 65N30 65N55 |
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