Efficient partitioning of conforming virtual element discretizations for large scale discrete fracture network flow parallel solvers

Discrete Fracture Network models are largely used for large scale geological flow simulations in fractured media. For these complex simulations, it is worth investigating suitable numerical methods and tools for efficient parallel solutions on High Performance Computing systems. In this paper we propose and compare different partitioning strategies, that result to be highly efficient and scalable, overperforming the classical mesh partitioning approach used to balance the workload of a conforming mesh among several processes. The proposed DFN-based partitioning strategies rely on the distribution of the fractures among parallel processes. The computational cost of the DFN-based partitionings is very small compared to the cost of classical mesh partitioning and the numerical results prove their effectiveness and good performances in solving linear systems for realistic DFN flow simulations.