Parallel Multigrid Preconditioning of the Conjugate Gradient Method for Systems of Subsurface Hydrology

Parallel preconditioners are considered for improving the convergence rate of the conjugate gradient method for solving sparse symmetric positive definite systems generated by finite element models of subsurface flow. The difficulties of adapting effective sequential preconditioners to the parallel environment are illustrated by our treatment of incomplete Cholesky preconditioning. These difficulties are avoided with multigrid preconditioning, which can be extended naturally to many processors so that the preconditioner remains global and effective.The coarse grid correction which defines the multigrid preconditioner is outlined and its parallel implementation with the distributed finite element data structure is presented, along with some examples of its use as a parallel preconditioner.