A major computational issue in the finite element (FE) integration of coupled consolidation equations is the repeated solution in time of the resulting discretized indefinite system. Because of ill-conditioning, the iterative solution, which is recommended in large size 3D settings, requires the computation of a suitable preconditioner to guarantee convergence. In this paper the coupled system is solved by a Krylov subspace method preconditioned by an inexact constraint preconditioner (ICP) preserving the same block structure as the native FE matrix. The conditioning number of the preconditioned coupled problem depends on the quality of the approximation of the block corresponding to the structural stiffness matrix. An efficient algorithm to implement ICP into a Krylov subspace method is developed. Numerical tests performed on realistic 3D problems reveal that ICP typically outperforms standard ILUT preconditioners and proves much more robust in severely ill-conditioned problems.

Novel preconditioners for the iterative solution to FE-discretized coupled consolidation equations

BERGAMASCHI, LUCA;FERRONATO, MASSIMILIANO;GAMBOLATI, GIUSEPPE
2007

Abstract

A major computational issue in the finite element (FE) integration of coupled consolidation equations is the repeated solution in time of the resulting discretized indefinite system. Because of ill-conditioning, the iterative solution, which is recommended in large size 3D settings, requires the computation of a suitable preconditioner to guarantee convergence. In this paper the coupled system is solved by a Krylov subspace method preconditioned by an inexact constraint preconditioner (ICP) preserving the same block structure as the native FE matrix. The conditioning number of the preconditioned coupled problem depends on the quality of the approximation of the block corresponding to the structural stiffness matrix. An efficient algorithm to implement ICP into a Krylov subspace method is developed. Numerical tests performed on realistic 3D problems reveal that ICP typically outperforms standard ILUT preconditioners and proves much more robust in severely ill-conditioned problems.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/2472920
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