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Generalized Eigenvalue Problem (generalized + eigenvalue_problem)

Distribution by Scientific Domains
Engineering83%

Selected Abstracts

A comparison of eigensolvers for large-scale 3D modal analysis using AMG-preconditioned iterative methods

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2005
Peter Arbenz
Abstract The goal of our paper is to compare a number of algorithms for computing a large number of eigenvectors of the generalized symmetric eigenvalue problem arising from a modal analysis of elastic structures. The shift-invert Lanczos algorithm has emerged as the workhorse for the solution of this generalized eigenvalue problem; however, a sparse direct factorization is required for the resulting set of linear equations. Instead, our paper considers the use of preconditioned iterative methods. We present a brief review of available preconditioned eigensolvers followed by a numerical comparison on three problems using a scalable algebraic multigrid (AMG) preconditioner. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Linear stability analysis of flow in a periodically grooved channel

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2003
T. Adachi1
Abstract We have conducted the linear stability analysis of flow in a channel with periodically grooved parts by using the spectral element method. The channel is composed of parallel plates with rectangular grooves on one side in a streamwise direction. The flow field is assumed to be two-dimensional and fully developed. At a relatively small Reynolds number, the flow is in a steady-state, whereas a self-sustained oscillatory flow occurs at a critical Reynolds number as a result of Hopf bifurcation due to an oscillatory instability mode. In order to evaluate the critical Reynolds number, the linear stability theory is applied to the complex laminar flow in the periodically grooved channel by constituting the generalized eigenvalue problem of matrix form using a penalty-function method. The critical Reynolds number can be determined by the sign of a linear growth rate of the eigenvalues. It is found that the bifurcation occurs due to the oscillatory instability mode which has a period two times as long as the channel period. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Frequency/time-domain modelling of 3D waveguide structures by a BI-RME approach

INTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 1 2002
P. Arcioni
This paper presents a full wave method for the determination of the mathematical model of a 3D waveguide structure in the form of the pole expansion in the s -plane of its generalized admittance matrix. The method is based on a boundary integral-resonant mode expansion approach. By the introduction of appropriate state-variables, the method leads to the pole expansion by solving a linear generalized eigenvalue problem, like in the well-known techniques used up to now in frequency/time domain modelling based on finite difference or finite element methods. With respect to these methods we have the advantage of a significant reduction in both memory allocation and computing time. Two examples show the accuracy of the results and the efficiency of the method. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Harmonic and refined Rayleigh,Ritz for the polynomial eigenvalue problem

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 1 2008
Michiel E. Hochstenbach
Abstract After reviewing the harmonic Rayleigh,Ritz approach for the standard and generalized eigenvalue problem, we discuss several extraction processes for subspace methods for the polynomial eigenvalue problem. We generalize the harmonic and refined Rayleigh,Ritz approaches which lead to new approaches to extract promising approximate eigenpairs from a search space. We give theoretical as well as numerical results of the methods. In addition, we study the convergence of the Jacobi,Davidson method for polynomial eigenvalue problems with exact and inexact linear solves and discuss several algorithmic details. Copyright © 2008 John Wiley & Sons, Ltd. [source]

,2 suboptimal estimation and control for nonnegative dynamical systems

OPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 1 2009
Wassim M. Haddad
Abstract Linear matrix inequalities (LMIs) provide a powerful design framework for linear control problems. In this paper, we use LMIs to develop ,2 (sub)optimal estimators and controllers for nonnegative dynamical systems. Specifically, we formulate a series of generalized eigenvalue problems subject to a set of LMI constraints for designing ,2 suboptimal estimators, static controllers, and dynamic controllers for nonnegative dynamical systems. The resulting ,2 suboptimal controllers guarantee that the closed-loop plant system states remain in the nonnegative orthant of the state space. Finally, a numerical example is provided to demonstrate the efficacy of the proposed approach. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Mixing symbolic and numerical approaches for the surface-to-surface intersection problem

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2007
Mario Fioravanti
This paper shows how the efficiency of the current methodologies applied to the surface-to-surface intersection problem can be improved by combining an algebraic/symbolic framework with efficient and robust numerical techniques. The algebraic/symbolic framework is used to translate the computation of resultants, subresultants, discriminants, etc. to one or several generalized eigenvalue problems and SVD computations. The framework requires only the values of the involved polynomials at some set of points, and it will guide the numerical computations, providing thus a certificate of the topological correctness of the output. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]