An efficient algorithm for solving elliptic problems on percolation clusters
Chenlin Gu · The Annals of Applied Probability · 2022
We present an efficient algorithm to solve elliptic Dirichlet problems defined on the cluster of supercritical Zd-Bernoulli percolation, as a generalization of the iterative method proposed by S. Armstrong, A. Hannukainen, T. Kuusi and J.-C. Mourrat (ESAIM Math. Model. Numer. Anal. (2021) 55 37–55). We also explore the two-scale expansion on the infinite cluster of percolation, and use it to give a rigorous analysis of the algorithm.