AN EFFICIENT ALGORITHM FOR SOLVING ELLIPTIC PROBLEMS ON PERCOLATION CLUSTERS

被引：0
作者：
Gu, Chenlin [1 ]
机构：
[1] PSL Univ, Ecole Normale Super, DMA, Paris, France
来源：
ANNALS OF APPLIED PROBABILITY | 2022年 / 32卷 / 04期
关键词：
Numerical algorithm; stochastic homogenization; percolation; QUENCHED INVARIANCE-PRINCIPLES; FINITE-ELEMENT METHODS; STOCHASTIC HOMOGENIZATION; LARGE DEVIATIONS; DISCRETE; REGULARITY; EQUATIONS; APPROXIMATION; COEFFICIENTS; CONVERGENCE;
D O I：
10.1214/21-AAP1748
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
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.
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页码：2755 / 2810
页数：56
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