Poisson equation in domains with concentrated holes

We consider solutions $u^{\epsilon }$ of Poisson problems with the Dirichlet condition on domains ${\mathrm{\Omega }}_{\epsilon }$ with holes concentrated at subsets of a domain $\mathrm{\Omega }$ non-periodically. We show $u^{\epsilon }$ converges to a solution of a Poisson problem with a simple function potential. This is a generalized result of a sample model given by Cioranescu and Murat (1997). They showed a result for case that holes are distributed at $\mathrm{\Omega }$ periodically.