%0 Journal Article %1 snchez2004newtonkrylov %A Sánchez, J. %A Net, M. %A Garcı́a-Archilla, B. %A Simó, C. %D 2004 %J Journal of Computational Physics %K 37l15-stability-problems-for-infinite-dimensional-dissipative-systems 37n10-dynamical-systems-in-fluid-mechanics-oceanography-fluid-mechanics 65p30-numerical-problems-in-dynamical-systems-bifurcation 76d05-incompressible-navier-stokes-equations %N 1 %P 13 - 33 %R 10.1016/j.jcp.2004.04.018 %T Newton–Krylov continuation of periodic orbits for Navier–Stokes flows %U http://www.sciencedirect.com/science/article/pii/S0021999104001895 %V 201 %X Efficient numerical algorithms for the continuation of periodic orbits of high-dimensional dissipative dynamical systems, and for analyzing their stability are presented. They are based on shooting, Newton–Krylov and Arnoldi methods. A thermal convection fluid dynamics problem, which has a rich bifurcation diagram due to symmetries, has been used as test. After a pseudo-spectral discretization of the equations a system of dimension O(104) has been obtained. The efficiency of the algorithms, which allows the unfolding of a complex diagram of periodic orbits, makes the methods suitable for the study of large nonlinear dissipative partial differential equations.

@article{snchez2004newtonkrylov, abstract = {Efficient numerical algorithms for the continuation of periodic orbits of high-dimensional dissipative dynamical systems, and for analyzing their stability are presented. They are based on shooting, Newton–Krylov and Arnoldi methods. A thermal convection fluid dynamics problem, which has a rich bifurcation diagram due to symmetries, has been used as test. After a pseudo-spectral discretization of the equations a system of dimension O(104) has been obtained. The efficiency of the algorithms, which allows the unfolding of a complex diagram of periodic orbits, makes the methods suitable for the study of large nonlinear dissipative partial differential equations.}, added-at = {2021-01-28T01:23:00.000+0100}, author = {Sánchez, J. and Net, M. and Garcı́a-Archilla, B. and Simó, C.}, biburl = {https://www.bibsonomy.org/bibtex/2f9840d8f2e8ebf06bbc7f23f09eb0c98/gdmcbain}, description = {Newton–Krylov continuation of periodic orbits for Navier–Stokes flows - ScienceDirect}, doi = {10.1016/j.jcp.2004.04.018}, interhash = {f739b99f3b6d1a00db0b621413c9361f}, intrahash = {f9840d8f2e8ebf06bbc7f23f09eb0c98}, issn = {0021-9991}, journal = {Journal of Computational Physics}, keywords = {37l15-stability-problems-for-infinite-dimensional-dissipative-systems 37n10-dynamical-systems-in-fluid-mechanics-oceanography-fluid-mechanics 65p30-numerical-problems-in-dynamical-systems-bifurcation 76d05-incompressible-navier-stokes-equations}, number = 1, pages = {13 - 33}, timestamp = {2021-01-28T01:24:28.000+0100}, title = {Newton–Krylov continuation of periodic orbits for Navier–Stokes flows}, url = {http://www.sciencedirect.com/science/article/pii/S0021999104001895}, volume = 201, year = 2004 }