Newton-Krylov-Schwarz methods for Richards' equation

Abstract : This paper discusses the design and implementation of a Newton-Krylov-Schwarz solver for the implicit temporal integration on an unstructured three-dimensional spatial mesh of Richards' equation for groundwater flow in unsaturated porous media. We use aggregation techniques from the algebraic multigrid literature to construct a coarse mesh for two-level Schwarz methods. Our coarse mesh differs from other constructions in that no coarse mesh geometry need be created and we do not need geometric information about the subdomains. We report on a computational example to illustrate the performance of the preconditioner.