Matrix-Dependent Multigrid Homogenization for Diffusion Problems

For problems with strongly varying or discontinuous diiusion coeecients we present a method to compute coarse-scale operators and to approximately determine the eeective diiusion tensor on the coarse-scale level. The approach is based on techniques that are used in multigrid, such as matrix-dependent prolongations and the construction of coarse-grid operators by means of the Galerkin approximation. In numerical experiments we compare our multigrid-homogenization method with continuous homogenization, renormalization and simple averaging approaches.