AN EFFICIENT ALGORITHM FOR SOLVING ELLIPTIC PROBLEMS ON PERCOLATION CLUSTERS
ANNALS OF APPLIED PROBABILITY(2022)
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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关键词
Numerical algorithm, stochastic homogenization, percolation
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