Large-scale Simulations of 3D Groundwater Flow Using Parallel Geometric Multigrid Method

Abstract

The multigrid method used with OpenMP/MPI hybrid parallel programming models is expected to play an important role in large-scale scientific computing on post-peta/exa-scale supercomputer systems. In the present work, the effect of sparse matrix storage formats on the performance of parallel geometric multigrid solvers was evaluated, and a new data structure for the Ellpack-Itpack (ELL) format is proposed. The proposed method is implemented for pGW3D-FVM, a parallel code for 3D groundwater flow simulations using the multigrid method, and the robustness and performance of the code was evaluated on up to 4,096 nodes (65,536 cores) of the Fujistu FX10 supercomputer system at the University of Tokyo. The parallel multigrid solver using the ELL format with coarse grid aggregation provided excellent performance improvement in both weak scaling (13%–35%) and strong scaling (40%–70%) compared to the original code using the CRS format.