We present an efficient algorithm to solve elliptic Dirichlet problems defined on the cluster of $\mathbb{ Z}^d$ 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.
Categories: math.PR cs.NA math.AP math.NA