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Title: Block constrained versus generalized Jacobi preconditioners for iterative solution of large-scale Biot's fem equations
Authors: Phoon, K.K. 
Toh, K.C. 
Chen, X. 
Keywords: Biot's consolidation equations
Block constrained preconditioner Generalized Jacobi preconditioner
Symmetric quasi-minimal residual (SQMR) method
Three-dimensional finite-element discretization
Issue Date: Nov-2004
Citation: Phoon, K.K., Toh, K.C., Chen, X. (2004-11). Block constrained versus generalized Jacobi preconditioners for iterative solution of large-scale Biot's fem equations. Computers and Structures 82 (28 SPEC. ISS.) : 2401-2411. ScholarBank@NUS Repository.
Abstract: Generalized Jacobi (GJ) diagonal preconditioner coupled with symmetric quasi-minimal residual (SQMR) method has been demonstrated to be efficient for solving the 2 × 2 block linear system of equations arising from discretized Biot's consolidation equations. However, one may further improve the performance by employing a more sophisticated non-diagonal preconditioner. This paper proposes to employ a block constrained preconditioner Pc that uses the same 2 × 2 block matrix but its (1, 1) block is replaced by a diagonal approximation. Numerical results on a series of 3-D footing problems show that the SQMR method preconditioned by Pc is about 55% more efficient time-wise than the counterpart preconditioned by GJ when the problem size increases to about 180,000 degrees of freedom. Over the range of problem sizes studied, the Pc-preconditioned SQMR method incurs about 20% more memory than the GJ-preconditioned counterpart. The paper also addresses crucial computational and storage issues in constructing and storing P c efficiently to achieve superior performance over GJ on the commonly available PC platforms. © 2004 Elsevier Ltd. All rights reserved.
Source Title: Computers and Structures
ISSN: 00457949
DOI: 10.1016/j.compstruc.2004.04.012
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