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Block preconditioning for fault/fracture mechanics saddle-point problems. (English) Zbl 1440.74473
Summary: The efficient simulation of fault and fracture mechanics is a key issue in several applications and is attracting a growing interest by the scientific community. Using a formulation based on Lagrange multipliers, the Jacobian matrix resulting from the Finite Element discretization of the governing equations has a non-symmetric generalized saddle-point structure. In this work, we propose a family of block preconditioners to accelerate the convergence of Krylov methods for such problems. We critically review possible advantages and difficulties of using various Schur complement approximations, based on both physical and algebraic considerations. The proposed approaches are tested in a number of real-world applications, showing their robustness and efficiency also in large-size and ill-conditioned problems.
Reviewer: Reviewer (Berlin)

MSC:
74S99 Numerical and other methods in solid mechanics
65F08 Preconditioners for iterative methods
74R10 Brittle fracture
Software:
DEMPack; FSAIPACK; TetGen
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