An Algorithm for Generalized Matrix Eigenvalue Problems

Moler, Cleve B.; Stewart, G. W.

doi:10.1137/0710024

Cited by 949 publications

(430 citation statements)

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“…For the parameters ϭ 0, the four conditions (15)- (18) at the virtual interface used, convergence is achieved for N 1 ϭ 20, N 21 ϭ 10, and y ϭ v, and finally 2 the three conditions (15), (17), and (18) N 22 ϭ 50; i.e., using more polynomials does not affect the at the virtual interface y ϭ h. Due to these rows, the QZfirst three digits of the most unstable eigenvalue (Table I). algorithm [17,18] will give 11 infinite eigenvalues, which…”

Section: Illustration Of Numerical Resultsmentioning

confidence: 99%

A Chebyshev Collocation Method for Solving Two-Phase Flow Stability Problems

Boomkamp

Boersma

Miesen

et al. 1997

Journal of Computational Physics

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Section: Illustration Of Numerical Resultsmentioning

confidence: 99%

A Chebyshev Collocation Method for Solving Two-Phase Flow Stability Problems

Boomkamp

Boersma

Miesen

et al. 1997

Journal of Computational Physics

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“…The eigenvalue problem associated with the infinite region is solved by two-dimensional finite element discretization using the QZ algorithm originally developed by Moler and Stewart. 27 Selected results of analytical studies carried out by using the formulation and the computer program mentioned in the preceding paragraphs are presented here. A BEM model of the three-dimensional rectangular reservoir is considered first in order to compare the analytical results with classical results obtained from a corresponding 2D model.…”

Section: Analytical Resultsmentioning

confidence: 99%

Three‐dimensional boundary element reservoir model for seismic analysis of arch and gravity dams

Jablonski

Humar

1990

Earthq Engng Struct Dyn

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/npsi/ctrl?lang=en http://nparc.cisti-icist.nrc-cnrc.gc.ca/npsi/ctrl?lang=fr Access and use of this website and the material on it are subject to the Terms and Conditions set forth at http://nparc.cisti-icist.nrc-cnrc.gc.ca/npsi/jsp/nparc_cp.jsp?lang=en NRC Publications Archive Archives des publications du CNRCThis publication could be one of several versions: author's original, accepted manuscript or the publisher's version. / La version de cette publication peut être l'une des suivantes : la version prépublication de l'auteur, la version acceptée du manuscrit ou la version de l'éditeur.Earthquake Engineering and Structural Dynamics, 19, 3, pp. 359-376, 1990-04 Three-dimensional boundary element reservoir model for seismic analysis of arch and gravity dams Jablonski, A. M.; Humar, J. L. THREE-DIMENSIONAL BOUNDARY ELEMENT RESERVOIR MODEL FOR SEISMIC ANALYSIS OF ARCH AND GRAVITY DAMS SUMMARYThe boundary element method has been successfully applied in the past to the analysis of hydrodynamic forces in twodimensional infinite as well as two-and three-dimensional finite reservoirs subjected to seismic ground motions. This paper presents the results of more recent research on the application of the constant boundary element method to the 3D analysis of reservoir vibration. Special boundary conditions, previously used in the 2D case, to treat infinite radiation damping and damping from foundation soil and banks have been incorporated in this formulation. Numerical results for vibration of a 3D infinite rectangular reservoir as well as of a 3D infinite reservoir impounded by an arch dam are presented and compared with some existing results obtained by other researchers.

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“…We discretize equations (2.6a)-(2.6b) using second-order centered finite differences and solve the resulting matrix eigenvalue problem using the "eig" function in Matlab, which uses the QZ algorithm (Moler & Stewart 1973). The grid resolution is dr = 0.025, giving 40 grid points per Rossby radii, thus resolving well the spatial scales normally associated with QG dynamics.…”

Section: Methods Of Solutionmentioning

confidence: 99%

Baroclinic instability of axially symmetric flow over sloping bathymetry

2016

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Observations and models of deep ocean boundary currents show that they exhibit complex variability, instabilities and eddy shedding, particularly over continental slopes that curve horizontally, for example around coastal peninsulas. In this article the authors investigate the source of this variability by characterizing the properties of baroclinic instability in mean flows over horizontally curved bottom slopes. The classical 2-layer quasi-geostrophic solution for linear baroclinic instability over sloping bottom topography is extended to the case of azimuthal mean flow in an annular channel. To facilitate comparison with the classical straight channel instability problem of uniform mean flow, the authors focus on comparatively simple flows in an annulus, namely uniform azimuthal velocity and solid-body rotation. Baroclinic instability in solid-body rotation flow is analytically analogous to the instability in uniform straight channel flow due to several identical properties of the mean flow, including vanishing strain rate and vorticity gradient. The instability of uniform azimuthal flow is numerically similar to straight channel flow instability as long as the mean barotropic azimuthal velocity is zero. Nonzero barotropic flow generally suppresses the instability via horizontal curvatureinduced strain and Reynolds stresses work. An exception occurs when the ratio of the bathymetric to isopycnal slopes is close to (positive) one, as is often observed in the ocean, in which case the instability is enhanced. A non-vanishing mean barotropic flow component also results in a larger number of growing eigenmodes and in increased non-normal growth. The implications of these findings for variability in deep western boundary currents are discussed.

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An Algorithm for Generalized Matrix Eigenvalue Problems

Cited by 949 publications

References 10 publications

A Chebyshev Collocation Method for Solving Two-Phase Flow Stability Problems

A Chebyshev Collocation Method for Solving Two-Phase Flow Stability Problems

Three‐dimensional boundary element reservoir model for seismic analysis of arch and gravity dams

Baroclinic instability of axially symmetric flow over sloping bathymetry

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