Multigrid Workbench: Fourier anlaysis of postsmoother

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Fourier analysis for postsmoother on finest level

Here the results of the postsmoother on the finest level are analyzed by Fourier techniques.

The Fourier analysis of presmoothing has shown that the high frequency error components have been reduced by the finest level smoothing. Now the coarse grid correction is added in to give an error decomposition of the form

Please watch the different scale (in comparison to the presmoother results).

After one smoothing step, the error becomes in the same representation

Clearly, now the error has been reduced significantly (by more than a factor of 0.1 in the full solution spectrum.

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Ulrich Ruede , Thu Feb 2 21:06:53 MEZ 1995
Updated by Craig C. Douglas