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Title:Large-scale Topology Optimization using Preconditioned Krylov Subspace Methods with Recycling
Author(s):Wang, Shun; de Sturler, Eric; Paulino, Glaucio H.
Subject(s):computer science
Abstract:The computational bottleneck of topology optimization is the solution of a large number of linear systems arising in the finite element analysis. We propose fast iterative solvers for large three-dimensional topology optimization problems to address this problem. Since the linear systems in the sequence of optimization steps change slowly from one step to the next, we can significantly reduce the number of iterations and the runtime of the linear solver by recycling selected search spaces from previous linear systems. In addition, we introduce a MINRES (Minimum Residual method) version with recycling (and a short term recurrence) to make recycling more efficient for symmetric problems. Furthermore, we discuss preconditioning to ensure fast convergence. We show that a proper rescaling of the linear systems reduces the huge condition numbers that typically occur in topology optimization to roughly those arising for a problem with constant density. We demonstrate the effectiveness of our solvers by solving a topology optimization problem with more than a million unknowns on a fast PC.
Issue Date:2006-01
Genre:Technical Report
Other Identifier(s):UIUCDCS-R-2006-2678
Rights Information:You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) days from the most recent time that you verified that this technical report is still available from the University of Illinois at Urbana-Champaign Computer Science Department under terms that include this permission. All other rights are reserved by the author(s).
Date Available in IDEALS:2009-04-20

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