Application of the Jacobi–Davidson method to accurate analysis of singular linear hydrodynamic stability problems

[1]  Carlos Tomei,et al.  Filtering the eigenvalues at infinite from the linear stability analysis of incompressible flows , 2007, J. Comput. Phys..

[2]  W. Arnoldi The principle of minimized iterations in the solution of the matrix eigenvalue problem , 1951 .

[3]  B. J. Boersma,et al.  A Chebyshev Collocation Method for Solving Two-Phase Flow Stability Problems , 1997 .

[4]  Thierry Braconnier,et al.  Convergence and round-off errors in a two-dimensional eigenvalue problem using spectral methods and Arnoldi-Chebyshev algorithm , 2006 .

[5]  Gerard L. G. Sleijpen,et al.  Jacobi-Davidson Style QR and QZ Algorithms for the Reduction of Matrix Pencils , 1998, SIAM J. Sci. Comput..

[6]  David W. Walker,et al.  Two Very Accurate and Efficient Methods for Computing Eigenvalues and Eigenfunctions in Porous Convection Problems , 1996 .

[7]  Gerard L. G. Sleijpen,et al.  A Jacobi-Davidson Iteration Method for Linear Eigenvalue Problems , 1996, SIAM J. Matrix Anal. Appl..

[8]  H. V. D. Vorst,et al.  Jacobi-davidson type methods for generalized eigenproblems and polynomial eigenproblems , 1995 .

[9]  Satish C. Reddy,et al.  A MATLAB differentiation matrix suite , 2000, TOMS.

[10]  K. Lindsay,et al.  A practical implementation of spectral methods resistant to the generation of spurious eigenvalues , 1992 .

[11]  B. Straughan Convection in a variable gravity field , 1989 .

[12]  Karl Meerbergen,et al.  Implicitly restarted Arnoldi with purification for the shift-invert transformation , 1997, Math. Comput..

[13]  Jack Dongarra,et al.  Chebyshev tau-QZ algorithm methods for calculating spectra of hydrodynamic stability problems , 1995 .

[14]  Dimitrios Giannakis,et al.  A spectral Galerkin method for the coupled Orr-Sommerfeld and induction equations for free-surface MHD , 2008, J. Comput. Phys..

[15]  G. Golub,et al.  Eigenvalue computation in the 20th century , 2000 .

[16]  Joost Rommes,et al.  Computing a partial generalized real Schur form using the Jacobi-Davidson method , 2007, Numer. Linear Algebra Appl..

[17]  C. I. Gheorghiu,et al.  Spectral methods in linear stability. Applications to thermal convection with variable gravity field , 2009 .

[18]  J. L. V. Dorsselaer,et al.  Pseudospectra for matrix pencils and stability of equilibria , 1997 .

[19]  Jens Markus Melenk,et al.  Spectral Galerkin Discretization for Hydrodynamic Stability Problems , 2000, Computing.

[20]  A. Zebib Removal of spurious modes encountered in solving stability problems by spectral methods , 1987 .

[21]  Brian Straughan,et al.  Linear and non‐linear stability thresholds for thermal convection in a box , 2006 .

[22]  Y. Saad,et al.  GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .

[23]  Robert L. Ash,et al.  Application of spectral collocation techniques to the stability of swirling flows , 1989 .

[24]  Joost Rommes,et al.  Arnoldi and Jacobi-Davidson methods for generalized eigenvalue problems Ax=λBx with singular B , 2007, Math. Comput..