On linearizations of the quadratic two-parameter eigenvalue problem

Hochstenbach, Michiel E.; Muhič, Andrej; Plestenjak, Bor

doi:10.1016/j.laa.2011.07.026

Cited by 25 publications

(33 citation statements)

References 10 publications

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“…Для нахождения всех решений проблемы (29), (31) ее можно представить как двухпараметрическую квадратичную проблему собственных значений с параметрами и , связанными формулой 2 = 2 + iRe( − ), и использовать методы, описанные в работе [26].…”

Section: задачи пространственной устойчивостиunclassified

“…Таким образом, проблема собственных значений (24) сводится к проблеме собственных значений (26), (27). Линеаризовав последнюю путем формирования сопровождающей матрицы, получим обыкновенную алгебраическую проблему собственных значений w = w,…”

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Asymptotic boundary conditions for the analysis of hydrodynamic stability of flows in regions with open boundaries

Бойко

Demyanko

Nechepurenko

2019

Russian Journal of Numerical Analysis and Mathematical Modelling

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A new approach to formulation of asymptotic boundary conditions for eigenvalue problems arising in numerical analysis of hydrodynamic stability of such shear flows as boundary layers, separations, jets, wakes, characterized by almost constant velocity of the main flow outside the shear layer or layers is proposed and justified. This approach makes it possible to formulate and solve completely the temporal and spatial stability problems in the locally-parallel approximation, reducing them to ordinary algebraic eigenvalue problems.

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Section: задачи пространственной устойчивостиunclassified

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Asymptotic boundary conditions for the analysis of hydrodynamic stability of flows in regions with open boundaries

Бойко

Demyanko

Nechepurenko

2019

Russian Journal of Numerical Analysis and Mathematical Modelling

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“…Any polynomial MEP can be made into a linear one (consisting of a zeroth-order term and first-order terms in each eigenvalue) via the process of linearization [30]. This process bears resemblance to the linearization of single-parameter polynomial eigenvalue problems; a process which is well-known [31].…”

Section: Linearizationmentioning

confidence: 99%

Multiparameter Spectral Analysis for Aeroelastic Instability Problems

Pons

Gutschmidt

2018

Journal of Applied Mechanics

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This paper presents a novel application of multiparameter spectral theory to the study of structural stability, with particular emphasis on aeroelastic flutter. Methods of multiparameter analysis allow the development of new solution algorithms for aeroelastic flutter problems; most significantly, a direct solver for polynomial problems of arbitrary order and size, something which has not before been achieved. Two major variants of this direct solver are presented, and their computational characteristics are compared. Both are effective for smaller problems arising in reduced-order modelling and preliminary design optimization. Extensions and improvements to this new conceptual framework and solution method are then discussed. * Corresponding author, adp53@cam.ac.uk, tel. +44 755 366 3296

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“…We will discuss both of these applications in Section 2. In the special case that k = 2 we speak of the quadratic multiparameter eigenvalue problem (QMEP); this problem has already been discussed in [6,11,15].…”

Section: Introductionmentioning

confidence: 99%

“…More details on possible linearizations for the quadratic case (k = 2) are given in [6]. The standard approach to solve a MEP of the form (2) is to consider the related coupled pair of generalized eigenvalue problems…”

Section: Introductionmentioning

confidence: 99%