An offline-online strategy for multiscale problems with random defects

In this paper, we propose an offline-online strategy based on the Localized Orthogonal Decomposition (LOD) method for elliptic multiscale problems with randomly perturbed diffusion coefficient. We consider a periodic deterministic coefficient local defects that occur probability p . The offline phase pre-computes entries to global LOD stiffness matrices single reference element (exploiting periodicity) selection of defect configurations. Given sample corresponding matrix is then computed by taking linear combinations pre-computed entries, in online phase. Our computable error estimates show yields good approximation solution small , which illustrated extensive numerical experiments. This makes proposed technique attractive already moderate sizes Monte Carlo simulation.