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The smoother on the third finest level (with 9 9 grid points) starts to work given the initial guess identical 0 and homogeneous (=0) Dirichlet boundary values.
However, the right hand side for this problem has been obtained by restricting the fine grid residuals, which are of course nonzero.
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
Essentially only two gridlines at the eastern boundary have been modified, because only close to this boundary nonzero right hand sides occur. Note however, that two lines on a 9 9 grid are twice as much in distance than on a 17 17 grid.
Together with a further coarse grid correction (and one postsmoothing sweep) this function is combined to a correction for the fine grid problem.
To presmoother on next coarser level To workbench home page.
Ulrich Ruede , Thu Feb 2 21:04:29 MEZ 1995
Updated by Craig C. Douglas