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Block-preconditioned Newton-Krylov solvers for fully coupled flow and geomechanics. (English) Zbl 1367.76034

Summary: The focus of this work is efficient solution methods for mixed finite element models of variably saturated fluid flow through deformable porous media. In particular, we examine preconditioning techniques to accelerate the convergence of implicit Newton-Krylov solvers. We highlight an approach in which preconditioners are built from block-factorizations of the coupled system. The key result of the work is the identification of effective preconditioners for the various sub-problems that appear within the block decomposition. We use numerical examples drawn from both linear and nonlinear hydromechanical models to test the robustness and scalability of the proposed methods. Results demonstrate that an algebraic multigrid variant of the block preconditioner leads to mesh-independent convergence, good parallel efficiency, and insensitivity to the material parameters of the medium.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76S05 Flows in porous media; filtration; seepage
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
86A05 Hydrology, hydrography, oceanography
74L10 Soil and rock mechanics
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