Eecient Parallel Multigrid Based Solvers for Large Scale Groundwater Flow Simulations

{ In this paper we present parallel solvers for large linear systems arising from the nite-element discretization of three-dimensional groundwater ow problems. We have tested our parallel implementations on the Intel Paragon XP/S 150 super-computer using up to 1024 parallel processors. Our solvers are based on multigrid and Krylov subspace methods. Our goal is to combine powerful algorithms and current generation high performance computers to enhance the capabilities of computer models for groundwater modeling. We show that multigrid can be a scalable algorithm on distributed memory machines. We demonstrate the eeectiveness of parallel multigrid based solvers by solving problems requiring more than 64 million nodes in less than a minute. Our results show that multigrid as a stand alone solver works best for problems with smooth coeecients, but for rough coeecients it is best used as a preconditioner for a Krylov subspace method. 1 Background In order to determine ow elds in a groundwater aquifer, a partial diierential equation (p.d.e) commonly referred to as the groundwater ow equation needs to be solved. For the steady-state saturated case, this equation is an elliptic p.d.e given by r (Krh) ? q = 0 (1) where K is the hydraulic conductivity tensor, h is the head eld, and q represents the source/sink terms coming from injection/pumping wells. In general, nite-element or nite-diierence techniques are used to discretize Equation (1). For many realistic problems, the groundwater ow equation involves rough coeecients (tensor K) resulting from heterogeneous hydraulic conductivity elds (or K-elds). In