Matrix Eigensystem Routines — EISPACK Guide Extension

Garbow, B. S.; Boyle, James M; Dongarra, Jack; Moler, Cleve B.

doi:10.1007/3-540-08254-9

Cited by 398 publications

(120 citation statements)

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“…(A1) by using the existing computer codes in Ref. [19], one needs to transform it into the following form [16]:…”

Section: Appendix: Determination Of Whirling Speeds and Mode Shapes Bmentioning

confidence: 99%

Analytical Solution for Whirling Speeds and Mode Shapes of a Distributed-Mass Shaft With Arbitrary Rigid Disks

Wu¹,

Lin²,

Shaw

2013

Journal of Applied Mechanics

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The purpose of this paper is to present an approach for replacing the effects of each rigid disk mounted on the spin shaft by a lumped mass together with a frequency-dependent equivalent mass moment of inertia so that the whirling motion of a rotating shaft-disk system is similar to the transverse free vibration of a stationary beam and the technique for the free vibration analysis of a stationary beam with multiple concentrated elements can be used to determine the forward and backward whirling speeds, along with mode shapes of a distributed-mass shaft carrying arbitrary rigid disks. Numerical results reveal that the characteristics of whirling motions are significantly dependent on the slopes of the associated natural mode shapes at the positions where the rigid disks are located. Furthermore, the results obtained from the presented analytical method and those obtained from existing literature or the finite element method (FEM) are in good agreement.

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“…(A1) by using the existing computer codes in Ref. [19], one needs to transform it into the following form [16]:…”

Section: Appendix: Determination Of Whirling Speeds and Mode Shapes Bmentioning

confidence: 99%

Analytical Solution for Whirling Speeds and Mode Shapes of a Distributed-Mass Shaft With Arbitrary Rigid Disks

Wu¹,

Lin²,

Shaw

2013

Journal of Applied Mechanics

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“…The latter can be solved numerically to obtain the band dispersion and the Bloch functions [25]. In our case, N G 100 leads to the requisite numerical precision in the diagonalization procedure for all the lattices.…”

Section: B Plane-wave Expansionmentioning

confidence: 99%

Superfluid drag of two-species Bose-Einstein condensates in optical lattices

Hofer

Bruder²,

Stojanović³

2012

Phys. Rev. A

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We study two-species Bose-Einstein condensates in quasi two-dimensional optical lattices of varying geometry and potential depth. Based on the numerically exact Bloch and Wannier functions obtained using the plane-wave expansion method, we quantify the drag (entrainment coupling) between the condensate components. This drag originates from the (short range) interspecies interaction and increases with the kinetic energy. As a result of the interplay between interaction and kinetic energy effects, the superfluid-drag coefficient shows a non-monotonic dependence on the lattice depth. To make contact with future experiments, we quantitatively investigate the drag for mass ratios corresponding to relevant atomic species.

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“…The reduced matrices were computed using PCGPAK [16]. All spectral radii were computed using the QZ algorithm in EISPACK [8,9].…”

Section: Numerical Experiments and Implementationmentioning

confidence: 99%

Iterative methods for cyclically reduced nonselfadjoint linear systems. II

Elman¹,

Golub²

1991

Math. Comp.

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Abstract.We perform an analytic and experimental study of line iterative methods for solving linear systems arising from finite difference discretizations of non-self-adjoint elliptic partial differential equations on two-dimensional domains. The methods consist of performing one step of cyclic reduction, followed by solution of the resulting reduced system by line relaxation. We augment previous analyses of one-line methods, and we derive a new convergence analysis for two-line methods, showing that both classes of methods are highly effective for solving the convection-diffusion equation. In addition, we compare the experimental performance of several variants of these methods, and we show that the methods can be implemented efficiently on parallel architectures.

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Matrix Eigensystem Routines — EISPACK Guide Extension

Cited by 398 publications

References 0 publications

Analytical Solution for Whirling Speeds and Mode Shapes of a Distributed-Mass Shaft With Arbitrary Rigid Disks

Analytical Solution for Whirling Speeds and Mode Shapes of a Distributed-Mass Shaft With Arbitrary Rigid Disks

Superfluid drag of two-species Bose-Einstein condensates in optical lattices

Iterative methods for cyclically reduced nonselfadjoint linear systems. II

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