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An efficient algorithm for solving elliptic problems on percolation clusters

by   Chenlin Gu, et al.
Cole Normale Suprieure

We present an efficient algorithm to solve elliptic Dirichlet problems defined on the cluster of Z^d supercritical Bernoulli percolation, as a generalization of the iterative method proposed by S. Armstrong, A. Hannukainen, T. Kuusi and J.-C. Mourrat. We also explore the two-scale expansion on the infinite cluster of percolation, and use it to give a rigorous analysis of the algorithm.


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