Abstract
Groundwater model calibration is becoming increasingly computationally time intensive. We describe a hybrid MPI/OpenMP approach to exploit two levels of parallelism in software and hardware to reduce calibration time on multicore computers with minimal parallelization effort. At first, HydroGeoChem 5.0 (HGC5) is parallelized using OpenMP for a uranium transport model with over a hundred species involving nearly a hundred reactions, and a field scale coupled flow and transport model. In the first application, a single parallelizable loop is identified to consume over 97% of the total computational time. With a few lines of OpenMP compiler directives inserted into the code, the computational time reduces about ten times on a compute node with 16 cores. The performance is further improved by selectively parallelizing a few more loops. For the field scale application, parallelizable loops in 15 of the 174 subroutines in HGC5 are identified to take more than 99% of the execution time. By adding the preconditioned conjugate gradient solver and BICGSTAB, and using a coloring scheme to separate the elements, nodes, and boundary sides, the subroutines for finite element assembly, soil property update, and boundary condition application are parallelized, resulting in a speedup of about 10 on a 16-core compute node. The Levenberg-Marquardt (LM) algorithm is added into HGC5 with the Jacobian calculation and lambda search parallelized using MPI. With this hybrid approach, compute nodes at the number of adjustable parameters (when the forward difference is used for Jacobian approximation), or twice that number (if the center difference is used), are used to reduce the calibration time from days and weeks to a few hours for the two applications. This approach can be extended to global optimization scheme and Monte Carol analysis where thousands of compute nodes can be efficiently utilized.