Research Group of Prof. Dr. M. Griebel
Institute for Numerical Simulation
[1] S. Knapek. Matrix-dependent multigrid homogenization for diffusion problems. SIAM J. Sci. Comp., 20(2):515-533, 1999.
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For problems with strongly varying or discontinuous diffusion coefficients we present a method to compute coarse-scale operators and to approximately determine the effective diffusion 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.