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.

引用

页码：2755 / 2810

页数：56

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