Coarse-grid operator ($A_H=R{A}_{h}P$)

A coarse-grid operator represents the equation solved for an error correction on the coarser level of a multigrid method. It may be obtained by rediscretizing the differential equation at the coarse spacing, or through the Galerkin coarse-grid operator formula displayed above. Here $R$ transfers residuals to the coarse grid and $P$ transfers coarse corrections to the fine grid. The right-side and operator scalings must be consistent with the chosen transfer convention.