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arXiv · 1608.02092

Computation of quasilocal effective diffusion tensors and connections to the mathematical theory of homogenization

Dietmar Gallistl·Daniel Peterseim
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Abstract

This paper aims at bridging existing theories in numerical and analytical homogenization. For this purpose the multiscale method of M{\aa}lqvist and Peterseim [Math. Comp. 2014], which is based on orthogonal subspace decomposition, is reinterpreted by means of a discrete integral operator acting on standard finite element spaces. The exponential decay of the involved integral kernel motivates the use of a diagonal approximation and, hence, a localized piecewise constant coefficient. In a periodic setting, the computed localized coefficient is proved to coincide with the classical homogenization limit. An a priori error analysis shows that the local numerical model is appropriate beyond the periodic setting when the localized coefficient satisfies a certain homogenization criterion, which can be verified a posteriori. The results are illustrated in numerical experiments.

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Dietmar Gallistl, Daniel Peterseim. 2016-08-06. Computation of quasilocal effective diffusion tensors and connections to the mathematical theory of homogenization. https://arxiv.org/abs/1608.02092

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