  This paper is concerned with the numerical solution of compressible fluid
flow in a fractured porous medium. The fracture represents a fast pathway
(i.e., with high permeability) and is modeled as a hypersurface embedded in the
porous medium. We aim to develop fast-convergent and accurate global-in-time
domain decomposition (DD) methods for such a reduced fracture model, in which
smaller time step sizes in the fracture can be coupled with larger time step
sizes in the subdomains. Using the pressure continuity equation and the
tangential PDEs in the fracture-interface as transmission conditions, three
different DD formulations are derived; each method leads to a space-time
interface problem which is solved iteratively and globally in time. Efficient
preconditioners are designed to accelerate the convergence of the iterative
methods while preserving the accuracy in time with nonconforming grids.
Numerical results for two-dimensional problems with non-immersed and partially
immersed fractures are presented to show the improved performance of the
proposed methods.
