Scalable algorithms for three-field mixed finite element coupled poromechanics.(English)Zbl 1373.76312
Summary: We introduce a class of block preconditioners for accelerating the iterative solution of coupled poromechanics equations based on a three-field formulation. The use of a displacement/velocity/pressure mixed finite-element method combined with a first order backward difference formula for the approximation of time derivatives produces a sequence of linear systems with a \(3 \times 3\) unsymmetric and indefinite block matrix. The preconditioners are obtained by approximating the two-level Schur complement with the aid of physically-based arguments that can be also generalized in a purely algebraic approach. A theoretical and experimental analysis is presented that provides evidence of the robustness, efficiency and scalability of the proposed algorithm. The performance is also assessed for a real-world challenging consolidation experiment of a shallow formation.
MSC:
| 76S05 | Flows in porous media; filtration; seepage |
| 74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65F08 | Preconditioners for iterative methods |
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References:
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