A multilevel Newton-Krylov interface solver for multiphysics couplings of flow in porous media

Ivan Yotov

Department of Mathematics, 301 Thackeray Hall, University of Pittsburgh, Pittsburgh, PA 15260


A multiblock approach to modeling flow in porous media allows for coupling different physical and numerical models in a single simulation through the use of mortar finite elements. The resulting nonlinear algebraic system is reduced to a nonlinear interface problem which is solved by a parallel Full Approximation Scheme (FAS) multigrid with a Newton-GMRES smoother. The efficiency of the method depends on the convergence of GMRES for computing the inexact Newton step. A physics-based Neumann-Neumann preconditioner is constructed for accelerating the GMRES convergence. Computational results from three dimensional multiphysics simulations illustrate the efficiency of the nonlinear interface solver.