English

An efficient algorithm for solving elliptic problems on percolation clusters

Probability 2019-08-01 v1 Numerical Analysis Analysis of PDEs Numerical Analysis

Abstract

We present an efficient algorithm to solve elliptic Dirichlet problems defined on the cluster of Zd\mathbb{Z}^d supercritical Bernoulli percolation, as a generalization of the iterative method proposed by S. Armstrong, A. Hannukainen, T. Kuusi and J.-C. Mourrat. We also explore the two-scale expansion on the infinite cluster of percolation, and use it to give a rigorous analysis of the algorithm.

Keywords

Cite

@article{arxiv.1907.13571,
  title  = {An efficient algorithm for solving elliptic problems on percolation clusters},
  author = {Chenlin Gu},
  journal= {arXiv preprint arXiv:1907.13571},
  year   = {2019}
}
R2 v1 2026-06-23T10:36:19.508Z