AN EFFICIENT ALGORITHM FOR SOLVING ELLIPTIC PROBLEMS ON PERCOLATION CLUSTERS

• 成果类型: Article
• 署名作者: Gu, Chenlin
• 署名单位: Universite PSL; Ecole Normale Superieure (ENS)
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/21-AAP1748
• 发表日期: 2022
• 页码: 2755-2810
• 关键词: quenched invariance-principles; finite-element methods; Stochastic Homogenization; large deviations; discrete; REGULARITY; EQUATIONS; approximation; coefficients; CONVERGENCE

摘要

We present an efficient algorithm to solve elliptic Dirichlet problems defined on the cluster of supercritical Z(d)-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.