Performance of Zero-Level Fill-In Preconditioning Techniques for Iterative Solutions with Geotechnical Applications
Publication: International Journal of Geomechanics
Volume 12, Issue 5
Abstract
Biot's symmetric indefinite linear systems of equations are commonly encountered in finite-element computations of geotechnical problems. The development of efficient solution methods for Biot's linear systems of equations is of practical importance to geotechnical software packages. In conjunction with the Krylov-subspace iterative method symmetric quasi-minimal residual (SQMR), some zero-level fill-in incomplete factorization preconditioning techniques including a symmetric successive overrelaxation (SSOR) type method and several zero-level incomplete LU [ILU(0)] methods are investigated and compared for Biot's symmetric indefinite linear systems of equations. Numerical experiments are carried out based on three practical geotechnical problems. Numerical results indicate that ILU(0) preconditioners are classical and generally efficient when adequately stabilized. However, the tunnel problem provides a counterexample demonstrating that ILU(0) preconditioners cannot be fully stabilized by preliminary scaling, reordering, making use of perturbed matrices, or dynamically selecting pivots. Compared with the investigated ILU(0) preconditioners, the recently proposed modified SSOR preconditioner is less efficient but is robust over the range of problems studied.
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Acknowledgments
The project is sponsored in part by the Scientific Research Foundation for the National Basic Research Program of China (Grant No. 2012CB026104) and the Fundamental Research Funds for the Central Universities (Grant No. 2011JBM070).
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Published In
International Journal of Geomechanics
Volume 12 • Issue 5 • October 2012
Pages: 596 - 605
Copyright
© 2012 American Society of Civil Engineers.
History
Received: Oct 20, 2010
Accepted: Mar 24, 2011
Published online: Mar 26, 2011
Published in print: Oct 1, 2012
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