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Partitioned versus global Krylov subspace iterative methods for FE solution of 3-D Biot’s problem. (English) Zbl 1173.74405
Summary: Finite element analysis of 3-D Biot’s consolidation problem needs fast solution of discretized large \(2\times 2\) block symmetric indefinite linear systems. In this paper, partitioned iterative methods and global Krylov subspace iterative methods are investigated and compared. The partitioned iterative methods considered include stationary partitioned iteration and non-stationary Prevost’s PCG procedure. The global Krylov subspace methods considered include MINRES and Symmetric QMR (SQMR). Two efficient preconditioners are proposed for global methods. Numerical experiments based on a pile-group problem and simple footing problems with varied soil profiles are carried out. Numerical results show that when used in conjunction with suitable preconditioners, global Krylov subspace iterative methods are more promising for large-scale computations, and further improvement could be possible if significant differences in the solid material properties are addressed in these preconditioned iterative methods.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76S05 Flows in porous media; filtration; seepage
65F10 Iterative numerical methods for linear systems
Software:
ILUT; QMRPACK
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References:
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