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We are interested in numerical algorithms for computing the electrical fieldgenerated by a charge distribution localized on scale $l$ in an infiniteheterogeneous correlated random medium, in a situation where the medium is onlyknown in a box of diameter $L\gg l$ around the support of the charge. We showthat the algorithm of Lu, Otto and Wang, suggesting optimal Dirichlet boundaryconditions motivated by the multipole expansion of Bella, Giunti and Otto,still performs well in correlated media. With overwhelming probability, weobtain a convergence rate in terms of $l$, $L$ and the size of the correlationsfor which optimality is supported with numerical simulations. These estimatesare provided for ensembles which satisfy a multi-scale logarithmic Sobolevinequality, where our main tool is an extension of the semi-group estimatesestablished by the first author. As part of our strategy, we constructsub-linear second-order correctors in this correlated setting which is ofindependent interest.

Artificial boundary conditions for random ellitpic systems with correlated coefficient field