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Krylov Subspace Methods (krylov + subspace_methods)

Distribution by Scientific Domains
Engineering75%

Selected Abstracts

Large-scale topology optimization using preconditioned Krylov subspace methods with recycling

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2007
Shun Wang
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. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Combining Krylov subspace methods and identification-based methods for model order reduction

INTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 6 2007
P. J. Heres
Abstract Many different techniques to reduce the dimensions of a model have been proposed in the near past. Krylov subspace methods are relatively cheap, but generate non-optimal models. In this paper a combination of Krylov subspace methods and orthonormal vector fitting (OVF) is proposed. In that way a compact model for a large model can be generated. In the first step, a Krylov subspace method reduces the large model to a model of medium size, then a compact model is derived with OVF as a second step. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Modified Hermitian and skew-Hermitian splitting methods for non-Hermitian positive-definite linear systems

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 3 2007
Liang Li
Abstract To further study the Hermitian and non-Hermitian splitting methods for a non-Hermitian and positive-definite matrix, we introduce a so-called lopsided Hermitian and skew-Hermitian splitting and then establish a class of lopsided Hermitian/skew-Hermitian (LHSS) methods to solve the non-Hermitian and positive-definite systems of linear equations. These methods include a two-step LHSS iteration and its inexact version, the inexact Hermitian/skew-Hermitian (ILHSS) iteration, which employs some Krylov subspace methods as its inner process. We theoretically prove that the LHSS method converges to the unique solution of the linear system for a loose restriction on the parameter ,. Moreover, the contraction factor of the LHSS iteration is derived. The presented numerical examples illustrate the effectiveness of both LHSS and ILHSS iterations. Copyright © 2007 John Wiley & Sons, Ltd. [source]