A parallel 2D stabilized finite element method for darcy flow on distributed systems

This paper discusses the high performance implementation of a 2D stabilized Mixed Finite Element Method (MFEM) for Darcy flow in a distributed memory system, using Message Passing Interface (MPI) specification. Darcy flow is involved in a wide range of problems related to earth sciences, such as ground waterflow, earth filled dams, soil liquefaction, petroleum engineering, etc. These problems involve huge amount of data for analysis. We propose a mesh partitioning algorithm based on reordered quadtree to solve the problem in parallel. The proposed algorithm first partitions the mesh over all processing elements and then parallelizes the system using the MPI specification. The conjugate gradient method augmented with preconditioning is used for the solution of the resulting system of stabilized mixed finite element equations for Darcy flow. Numerical experiments are conducted on a quad core Intel Xeon based computer cluster. Overall, a maximum of 12.24 speedup factor is achieved during the numerical simulations on 28 processors.