A Multigrid-Based Solver for Mixed Finite-Element Approximations to Groundwater Flow
Mixed finite-element methods have several features that are attractive in the
numerical simulation of groundwater flow. Chief among these is the possibility
of computing Darcy velocities whose accuracies are comparable to those
of the computed hydraulic heads. Much current research centers on solving
the large linear systems that arise from mixed finite-element discretizations.
We examine an iterative method that largely overcomes the poor conditioning
associated with fine spatial grids and highly variable aquifer properties.
The method incorporates a multigrid scheme inside an outer iteration whose
convergence rate is independent of grid mesh size and variations in hydraulic
conductivity. As we demonstrate, the multigrid algorithm is amenable to effective
parallelization on distributed-memory machines, making the overall
algorithm a highly efficient one in such computing environments.
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