Effective block diagonal preconditioners for Biot’s consolidation equations in piled-raft foundations

International Journal for Numerical and Analytical Methods in Geomechanics, Volume 37, Issue 8, pages 871–892, 10 June 2013.

 

K. B. Chaudhary, K. K. Phoon, K. C. Toh.

 

Department of Civil and Environmental Engineering, National University of Singapore, Singapore, Singapore and

Department of Mathematics, National University of Singapore, Singapore, Singapore.

 

Abstract

The finite element (FE) simulation of large-scale soil–structure interaction problems (e.g. piled-raft, tunnelling, and excavation) typically involves structural and geomaterials with significant differences in stiffness and permeability. The symmetric quasi-minimal residual solver coupled with recently developed generalized Jacobi, modified symmetric successive over-relaxation (MSSOR), or standard incomplete LU factorization (ILU) preconditioners can be ineffective for this class of problems. Inexact block diagonal preconditioners that are inexpensive approximations of the theoretical form are systematically evaluated for mitigating the coupled adverse effects because of such heterogeneous material properties (stiffness and permeability) and because of the percentage of the structural component in the system in piled-raft foundations. Such mitigation led the proposed preconditioners to offer a significant saving in runtime (up to more than 10 times faster) in comparison with generalized Jacobi, modified symmetric successive over-relaxation, and ILU preconditioners in simulating piled-raft foundations. Copyright © 2012 John Wiley & Sons, Ltd.

Copyright © 2012 John Wiley & Sons, Ltd.

 

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