The interpolation transports the correction obtained on the coarser grid to the fine grid. The typical process interpolates to neighboring values according to a distributive stencil, like
This is the bilinear interpolation, as used in the example of the multigrid workbench.
Alternatives include
which turns out to be the natural interpolation, when finite elements on a square mesh triangulation are used to discretize the operator.
In general, the choice of interpolation as the transpose of restriction plays an especially important role in the praxis and theory of multigrid methods.
Ulrich Ruede , Thu Feb 2 21:06:05 MEZ 1995
Updated by Craig C. Douglas