  We present a topology-based method for mesh-partitioning in three-dimensional
discrete fracture network (DFN) simulations that take advantage of the
intrinsic multi-level nature of a DFN. DFN models are used to simulate flow and
transport through low-permeability fractured media in the subsurface by
explicitly representing fractures as discrete entities. The governing equations
for flow and transport are numerically integrated on computational meshes
generated on the interconnected fracture networks. Modern high-fidelity DFN
simulations require high-performance computing on multiple processors where
performance and scalability depend partially on obtaining a high-quality
partition of the mesh to balance work-loads and minimize communication across
all processors. The discrete structure of a DFN naturally lends itself to
various graph representations. We develop two applications of the multilevel
graph partitioning algorithm to partition the mesh of a DFN. In the first, we
project a partition of the graph based on the DFN topology onto the mesh of the
DFN and in the second, this projection is used as the initial condition for
further partitioning refinement of the mesh. We compare the performance of
these methods with standard multi-level graph partitioning using graph-based
metrics (cut, imbalance, partitioning time), computational-based metrics
(FLOPS, iterations, solver time), and total run time. The DFN-based and the
mesh-based partitioning methods are comparable in terms of the graph-based
metrics, but the time required to obtain the partition is several orders of
magnitude faster using the DFN-based partitions. In combination, these
partitions are several orders of magnitude faster than the mesh-based
partition. In turn, this hybrid method outperformed both of the other methods
in terms of the total run time.
