Matrix-Dependent Multigrid-Homogenization For Diffusion Problems

Abstract

. 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 matrixdependent 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. Key words. homogenization, multigrid, matrix-dependent prolongation, Galerkin approximation, Schur complement AMS subject classification. 35B27, 65N55, 65N30 1. Introduction. Solutions for problems which model locally strong varying phenomena on a micro-scale level require that all length scales present in the problem are completely resolved. However, due to storage requirements and numerical complexity, the grid for numerical simul..