Efficient Solution of a Generalized Eigenvalue Problem Arising in a Thermoconvective Instability

作     者：M.C.Navarro H.Herrero A.M.Mancho A.Wathen 

作者机构：Departamento de MatematicasFacultad de Ciencias QuimicasUniversidad de Castilla-La Mancha13071 Ciudad RealSpain Departamento deMatematicasIMAFFConsejo Superior de Investigaciones Cientificas28006MadridSpain Numerical Analysis GroupComputing LaboratoryOxford UniversityOxford OX13QDUnited Kingdom. 

出 版 物：《Communications in Computational Physics》 (计算物理通讯（英文）)

年 卷 期：2008年第3卷第2期

页      面：308-329页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：the Research Grants MCYT(Spanish Government)MTM2006-14843-C02-01 and CCYT(JC Castilla-La Mancha)PAC-05-005 which include FEDER funds.AMM thanks support by Grants from CSIC(PI-200650I224) Comunidad de Madrid(SIMUMAT S-0505-ESP-0158) Junta de Castilla-La Mancha(PAC-05-005-2) 

主　　题：Rayleigh-Benard convection Chebyshev collocation preconditioners Arnoldi method Hopf bifurcation. 

摘      要：The aim of this paper is to develop an efficient numerical method to compute the eigenvalues of the stability analysis of a problem describing the motion of a fluid within a cylindrical container heated non-homogeneously from *** axisymmetric stationary motion settles in,at certain values of the external parameters appearing in the set of partial differential equations modeling the *** basic solution is computed by discretizing the equations with a Chebyshev collocation *** linear stability is formulated with a generalized eigenvalue *** numerical approach(generalized Arnoldi method)uses the idea of preconditioning the eigenvalue problem with a modified Cayley transformation before applying the Arnoldi *** works have dealt with transformations requiring regularity to one of the *** this article we extend those results to the case in which that submatrix is *** method allows a fast computation of the critical eigenvalues which determine whether the steady flow is stable or *** algorithm based on this method is compared to the QZ method and is found to be computationally more *** reliability of the computed eigenvalues in terms of stability is confirmed via pseudospectra calculations.