Iterative Solution of Large Sparse Linear Systems Arising from Application of Interior Point Method in Computational Geomechanics

The efficiency of several preconditioned Conjugate Gradient (PCG) schemes for solving of large sparse linear systems arising from application of second order cone programming in computational plasticity problems is studied. Direct solvers fail to solve these linear systems in large sizes, such as th...

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Bibliographic Details
Published inWorld Congress on Engineering Vol. 1; pp. 216 - 221
Main Authors Kardani, Omid, Lyamin, Andrei V, Krabbenhoeft, Kristian
Format Journal Article
LanguageEnglish
Published 01.01.2013
Subjects
Computation
Computational efficiency
Conjugate gradients
Convergence
Iterative methods
Linear systems
Preconditioning
Solvers
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Summary:The efficiency of several preconditioned Conjugate Gradient (PCG) schemes for solving of large sparse linear systems arising from application of second order cone programming in computational plasticity problems is studied. Direct solvers fail to solve these linear systems in large sizes, such as three dimensional cases, due to their high storage and computational cost. This motivates using iterative methods. However, iterative solvers are not efficient without preconditioning techniques for difficult problems. In this paper, the effect of different incomplete factorization preconditioning techniques on the convergence behavior of the preconditioned Conjugate Gradient (PCG) method to solve these large sparse and usually ill-conditioned linear systems is investigated. Furthermore, numerical results of applying PCG to several sample systems are presented and discussed. Several suggestions are also made as potential research subjects in this field.
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ISSN:2078-0958