solidot新版网站常见问题,请点击这里查看。

An embedded corrector problem for homogenization. Part I: Theory. (arXiv:1807.05131v1 [math.NA])

来源于:arXiv
This article is the first part of a two-fold study, the objective of which is the theoretical analysis and numerical investigation of new approximate corrector problems in the context of stochastic homogenization. We present here three new alternatives for the approximation of the homogenized matrix for diffusion problems with highly-oscillatory coefficients. These different approximations all rely on the use of an embedded corrector problem (that we previously introduced in [Canc\`es, Ehrlacher, Legoll and Stamm, C. R. Acad. Sci. Paris, 2015]), where a finite-size domain made of the highly oscillatory material is embedded in a homogeneous infinite medium whose diffusion coefficients have to be appropriately determined. The motivation for considering such embedded corrector problems is made clear in the companion article [Canc\`es, Ehrlacher, Legoll, Stamm and Xiang, in preparation], where a very efficient algorithm is presented for the resolution of such problems for particular hetero 查看全文>>