Recent Advances in Iterative Methods

Golub, Gene H.; Greenbaum, Anne; Luskin, Mitchell; Problems, Structured

doi:10.1007/978-1-4613-9353-5

Cited by 8 publications

(1 citation statement)

References 2 publications

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“…The following methods were studied: the conjugate gradient squared method (CGS) [9] the transpose-free quasi-minimal residual method (TFQMR) [10] the biconjugate gradient stabilized method (BiCGStab) [5] the generalized minimal residual method (GMRES) [6] The Jacobi preconditioner was used in every experiment. …”

Section: Experiments Settingmentioning

confidence: 99%

Linear solver performance in elastoplastic problem solution on GPU cluster

Khalevitsky¹,

Konovalov²,

Burmasheva³

et al. 2017

AIP Conference Proceedings

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Comparative study of Krylov Subspace method implementations for a GPU cluster in elastoplastic problems AIP Conference Proceedings 1785, 040024 (2016) Abstract. Applying the finite element method to severe plastic deformation problems involves solving linear equation systems. While the solution procedure is relatively hard to parallelize and computationally intensive by itself, a long series of large scale systems need to be solved for each problem. When dealing with fine computational meshes, such as in the simulations of three-dimensional metal matrix composite microvolume deformation, tens and hundreds of hours may be needed to complete the whole solution procedure, even using modern supercomputers. In general, one of the preconditioned Krylov subspace methods is used in a linear solver for such problems. The method convergence highly depends on the operator spectrum of a problem stiffness matrix. In order to choose the appropriate method, a series of computational experiments is used. Different methods may be preferable for different computational systems for the same problem. In this paper we present experimental data obtained by solving linear equation systems from an elastoplastic problem on a GPU cluster. The data can be used to substantiate the choice of the appropriate method for a linear solver to use in severe plastic deformation simulations.

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