Efficient parallel multigrid based solvers for large scale groundwater flow simulations

Abstract

In this paper, we present parallel solvers for large linear systems arising from the finite-element discretization of three-dimensional groundwater flow problems. We have tested our parallel implementations on the Intel Paragon XP/S 150 supercomputer 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 effectiveness 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 coefficients, but for rough coefficients it is best used as a preconditioner for a Krylov subspace method.