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The smoother on the finest level (with 33x33 grid points) starts to work given the initial guess where the solution is set to the known Dirichlet boundary values of the example problem and 0 everywhere else.
In our model algorithm two sweeps of the Gauß-Seidel method are applied. They sweep over the grid twice from left to right and front to back. The result is
Only the two gridlines closest to the nonzero boundary have been modified. However, the solution looks much smoother now. This becomes more apparent by Fourier Analysis.
The result of a V-cycle is obtained when the result of the coarse grid correction is added to this this smoothed approximation (and a final postsmoothing step has been applied).
To presmoother on next coarser level.
To workbench home page.
Ulrich Ruede , Thu Feb 2 21:04:18 MEZ 1995
Updated by Craig C. Douglas