Finite difference heterogeneous multi-scale method for homogenization problems
Journal of Computational Physics
Wavelet-based multi-scale projection method in homogenization of heterogeneous media
Finite Elements in Analysis and Design - Special issue: The fifteenth annual Robert J. Melosh competition
Numerical methods for multiscale elliptic problems
Journal of Computational Physics
Patch dynamics with buffers for homogenization problems
Journal of Computational Physics
Wavelet-based multi-scale coarse graining approach for DNA molecules
Finite Elements in Analysis and Design
Numerical upscaling for the eddy-current model with stochastic magnetic materials
Journal of Computational Physics
Upscaling methods for a class of convection-diffusion equations with highly oscillating coefficients
Journal of Computational Physics
A new wavelet multigrid method
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Computers & Mathematics with Applications
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A numerical homogenization procedure for elliptic differential equations is presented. It is based on wavelet decompositions of discrete operators in fine and coarse scale components followed by the elimination of the fine scale contributions. If the operator is in divergence form, this is preserved by the homogenization procedure. For periodic problems, results similar to classical effective coefficient theory are proved. The procedure can be applied to problems that are not cell-periodic.