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The solution of elliptic partial differential equations on composite overlapping grids using multigrid is discussed. An approach is described that provides a fast and memory efficient scheme for the solution of boundary value problems in complex geometries. The key aspects of the new scheme are an automatic coarse grid generation algorithm, an adaptive smoothing technique for adjusting residuals on different component grids, and the use of local smoothing near interpolation boundaries. Otherdoi:10.1137/040603735 fatcat:3h52i5estram5ja5nlwlcxomc4