Raju Ram, ITWM
Parallel Deflated Conjugate Gradient Method to Model Groundwater Flow in a Layered Grid
Groundwater, present beneath the earth’s surface in soil pore spaces, is the primary source of fresh water that we use in day to day life. Hydrologists at Dutch research institute Deltares are developing large groundwater models to support water managers in their decision-making process. These models use a Deltares accelerated version of MODFLOW called iMODFLOW. Together with the United State Geological Survey (USGS), Deltares has developed the Parallel Krylov Solver (PKS) package, which has recently been incorporated into iMODFLOW. It was observed that for the larger number of subdomains, the Preconditioned Conjugate Gradient (PCG) solver in PKS deteriorates the number of iterations.
We have implemented the deflation preconditioner with constant and linear deflation vectors in the PCG solver. These vectors approximate the eigenvectors that are slowing down convergence. The groundwater simulation time can be reduced by a factor of 4 using deflation in iMODFLOW. This speedup is achieved due to a decrease in the PCG iterations. The iteration drop is highest using linear deflation vectors.
In this talk, we present the mathematics behind deflation, implementation on a parallel computer and discuss the results.