%0 Generic %1 kelley2004newtonkrylov %A Kelley, C. T. %A Kevrekidis, I. G. %A Qiao, L. %D 2004 %K 65f10-iterative-methods-for-linear-systems 65h10-systems-of-nonlinear-algebraic-equations 65h17-nonlinear-algebraic-transcendental-equations-eigenvalues-eigenvectors 65h20-global-methods-including-homotopy-approaches 65l05-odes-ivps %T Newton-Krylov solvers for time-steppers %U http://arxiv.org/abs/math/0404374 %X We study how the Newton-GMRES iteration can enable dynamic simulators (time-steppers) to perform fixed-point and path-following computations.For a class of dissipative problems, whose dynamics are characterized by a slow manifold, the Jacobian matrices in such computations are compact perturbations of the identity. We examine the number of GMRES iterations required for each nonlinear iteration as a function of the dimension of the slow subspace and the time-stepper reporting horizon. In a path-following computation, only a small number (one or two) of additional GMRES iterations is required.

@misc{kelley2004newtonkrylov, abstract = {We study how the Newton-GMRES iteration can enable dynamic simulators (time-steppers) to perform fixed-point and path-following computations.For a class of dissipative problems, whose dynamics are characterized by a slow manifold, the Jacobian matrices in such computations are compact perturbations of the identity. We examine the number of GMRES iterations required for each nonlinear iteration as a function of the dimension of the slow subspace and the time-stepper reporting horizon. In a path-following computation, only a small number (one or two) of additional GMRES iterations is required.}, added-at = {2020-08-28T01:36:18.000+0200}, author = {Kelley, C. T. and Kevrekidis, I. G. and Qiao, L.}, biburl = {https://www.bibsonomy.org/bibtex/29c891025c744accc66c5c4301ba8d0a3/gdmcbain}, howpublished = {ArXiv:math/0404374}, interhash = {df7873cd3c4b51446b0a66764bf30acd}, intrahash = {9c891025c744accc66c5c4301ba8d0a3}, keywords = {65f10-iterative-methods-for-linear-systems 65h10-systems-of-nonlinear-algebraic-equations 65h17-nonlinear-algebraic-transcendental-equations-eigenvalues-eigenvectors 65h20-global-methods-including-homotopy-approaches 65l05-odes-ivps}, timestamp = {2020-08-28T01:38:12.000+0200}, title = {Newton-Krylov solvers for time-steppers}, url = {http://arxiv.org/abs/math/0404374}, year = 2004 }