Homogenization and multigrid - Neuß, Nicolas; Jäger, Willi; Wittum, Gabriel (Computing, 2001)
For elliptic partial differential equations with periodically oscillating coefficients which may have large jumps, we prove robust convergence of a two-grid algorithm using a prolongation motivated by the theory of homogenization. The corresponding Galerkin operator on the coarse grid turns out to be a discretization of a diffusion operator with homogenized coefficients obtained by solving discrete cell problems. This two-grid method is then embedded inside a multi-grid cycle extending over both the fine and the coarse scale.
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