Block constraint preconditioners are a most recent development for the iterative solution to large-scale, often ill-conditioned, coupled consolidation problems. A major limitation to their practical use, however, is the somewhat difficult selection of a number of user-defined parameters (at least 4) in a more or less optimal way. The present paper investigates the robustness of three variants of the block constraint preconditioning in relation to the above parameters. A theoretical analysis of the eigenspectrum of the preconditioned matrix provides relatively simple bounds of the eigenvalues as a function of these parameters. A number of test problems used to validate the theoretical results show that both the mixed constraint preconditioner (MCP) combined with the symmetric quasi-minimal residual (SQMR) solver and the MCP triangular variant (T-MCP) combined with the bi-conjugate gradient stabilized (Bi-CGSTAB) are efficient and robust tools for the solution to difficult Finite Element-discretized coupled consolidation problems. Moreover, the practical selection of the user-defined parameters is relatively easy as a stable behavior is observed for a wide range of fill-in degree values. The theoretical bounds on the eigenspectrum of the preconditioned matrix may help to suggest the most appropriate parameter combination.

Performance and robustness of block constraint preconditioners in finite element coupled consolidation problems

FERRONATO, MASSIMILIANO;BERGAMASCHI, LUCA;GAMBOLATI, GIUSEPPE
2010

Abstract

Block constraint preconditioners are a most recent development for the iterative solution to large-scale, often ill-conditioned, coupled consolidation problems. A major limitation to their practical use, however, is the somewhat difficult selection of a number of user-defined parameters (at least 4) in a more or less optimal way. The present paper investigates the robustness of three variants of the block constraint preconditioning in relation to the above parameters. A theoretical analysis of the eigenspectrum of the preconditioned matrix provides relatively simple bounds of the eigenvalues as a function of these parameters. A number of test problems used to validate the theoretical results show that both the mixed constraint preconditioner (MCP) combined with the symmetric quasi-minimal residual (SQMR) solver and the MCP triangular variant (T-MCP) combined with the bi-conjugate gradient stabilized (Bi-CGSTAB) are efficient and robust tools for the solution to difficult Finite Element-discretized coupled consolidation problems. Moreover, the practical selection of the user-defined parameters is relatively easy as a stable behavior is observed for a wide range of fill-in degree values. The theoretical bounds on the eigenspectrum of the preconditioned matrix may help to suggest the most appropriate parameter combination.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/2444958
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