An aggregation-based domain decomposition preconditioner for groundwater flow

We consider theoretical and computational issues associated with an aggrega tion-based domain decomposition preconditioner applied to a Bi-CGSTAB itera tive solver used to solve both Laplace's equation and an important nonlinea r model from hydrology used to simulate unsaturated flow, Richards equation . Theoretical results for Laplace's equation provide estimates of the condi tion number and the rate of convergence for a two-level Schwarz domain deco mposition preconditioner. Computational results for Laplace's equation and Richards' equation show excellent scalability, although no theory is yet av ailable to support the results for the difficult nonlinear problem.