  Traditional two level upscaling techniques suffer from a high offline cost
when the coarse grid size is much larger than the fine grid size. Thus,
multilevel methods are desirable for problems with complex heterogeneities and
high contrast. In this paper, we propose a novel three-level upscaling method
for flow problems in fractured porous media. Our method starts with a fine grid
discretization for the system involving fractured porous media. In the next
step, based on the fine grid model, we construct a nonlocal multi-continua
upscaling (NLMC) method using an intermediate grid. The system resulting from
NLMC gives solutions that have physical meaning. In order to enhance locality,
the grid size of the intermediate grid needs to be relatively small, and this
motivates using such an intermediate grid. However, the resulting NLMC upscaled
system has a relatively large dimension. This motivates a further step of
dimension reduction. In particular, we will apply the idea of the Generalized
Multiscale Finite Element Method (GMsFEM) to the NLMC system to obtain a final
reduced model. We present simulation results for a two-dimensional model
problem with a large number of fractures using the proposed three-level method.
