An efficient parallel method for large-scale groundwater flow equation based on PETSc

In this paper, we present an efficient scheme for the parallel solution of large-scale three-dimensional groundwater flow equation. The scheme has been implemented and the program is parallelized by using a SPMD (single-program, multiple data) paradigm and a domain decomposition strategy provided in PETSc (Portable Extensible Toolkit for Scientific Computation). The efficiency and scalability of the parallel-computing scheme are demonstrated by completing a simplified groundwater scenario, in which different preconditioned Krylov subspace methods have been tested and analyzed. The numerical results show that the parallel method could enhance the modeling capabilities and accelerate the simulation process significantly.