Abstract
We present an efficient algorithm to solve elliptic Dirichlet problems defined on the cluster of supercritical -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.
Acknowledgments
The author would like to thank Jean–Christophe Mourrat for his suggestion to study this topic and helpful discussions, and Paul Dario for inspiring discussions. The author is supported by the PhD scholarship from Ecole Polytechnique.
Citation
Chenlin Gu. "An efficient algorithm for solving elliptic problems on percolation clusters." Ann. Appl. Probab. 32 (4) 2755 - 2810, August 2022. https://doi.org/10.1214/21-AAP1748
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