Parallel Deflated CG Method to Model Groundwater Flow in a Layered Grid

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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 man- agers in their decision-making process. For example, these models simulate effects such as water availability during periods of drought. These models use a Deltares accelerated version of MODFLOW called iMODFLOW.

Together with the United State Geological Survey (USGS), Deltares has devel- oped the Parallel Krylov Solver (PKS) package, which has recently been incorpo- rated 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 de- flation 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 in iMODFLOW. This speed up is achieved due to a decrease in PCG iterations. The iteration drop is highest using linear deflation vectors.