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On the coarsest level (with 3 3 grid points) the problem has only one (inner) unknown left, all others are Dirichlet boundary values. Therefore a single sweep of the Gauß-Seidel method will act as an exact solver. The result is
This solution is interpolated and combined with the result of the previous smoother on the next finer level and becomes a correction for the still finer grid problems.
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Ulrich Ruede , Thu Feb 2 21:04:39 MEZ 1995
Updated by Craig C. Douglas