Computation of invariant tori by Newton–Krylov methods in large-scale dissipative systems
A method to compute invariant tori in high-dimensional systems, obtained as discretizations of PDEs, by continuation and Newton–Krylov methods is described. Invariant tori are found as fixed points of a generalized Poincaré map so that the dimension of the system of equations to be solved is that of...
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| Veröffentlicht in: | Physica. D 2010-02, Vol.239 (3), p.123-133 |
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| container_title | Physica. D |
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| creator | Sánchez, J. Net, M. Simó, C. |
| description | A method to compute invariant tori in high-dimensional systems, obtained as discretizations of PDEs, by continuation and Newton–Krylov methods is described. Invariant tori are found as fixed points of a generalized Poincaré map so that the dimension of the system of equations to be solved is that of the original system. Due to the dissipative nature of the problems studied, the convergence of the linear solvers is extremely fast. The computation of periodic orbits inside the Arnold’s tongues is also considered. Thermal convection of a binary mixture of fluids, in a rectangular cavity, has been used to test the method. |
| doi_str_mv | 10.1016/j.physd.2009.10.012 |
| format | Article |
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Thermal convection of a binary mixture of fluids, in a rectangular cavity, has been used to test the method.</description><subject>Continuation methods</subject><subject>Exact sciences and technology</subject><subject>Generalized Poincaré map</subject><subject>Invariant tori</subject><subject>Newton–Krylov methods</subject><subject>Physics</subject><subject>Resonances</subject><subject>Variational equations</subject><issn>0167-2789</issn><issn>1872-8022</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><recordid>eNp9kL2O1DAUhS0EEsPCE9C4gS6z13YmdgoKNOJPrKCBisLyONesR0kcfD2D0vEOvCFPQrKzoqS60tF3ztU5jD0XsBUgmuvjdrqdqdtKgHZRtiDkA7YRRsvKgJQP2WahdCW1aR-zJ0RHABBa6Q37tk_DdCquxDTyFHgczy5HNxZeUo78MPNP-LOk8c-v3x_z3KczH7Dcpo4Wkvcuf8eKvOuRd5EoTkvOGTnNVHCgp-xRcD3hs_t7xb6-ffNl_766-fzuw_71TeVVU5dqJ9ArMK5F1RwEmINAdCZAZzQGpWspTFNL1dY1qNoYDQoPGGTQKLoAYNQVe3nJnXL6cUIqdojkse_diOlEVu2EgJ1aQXUBfU5EGYOdchxcnq0Auw5pj_ZuSLsOuYrLkIvrxX28W6uG7EYf6Z9VSgWtadb0VxcOl67niNmSjzh67GJGX2yX4n___AUX74w6</recordid><startdate>20100201</startdate><enddate>20100201</enddate><creator>Sánchez, J.</creator><creator>Net, M.</creator><creator>Simó, C.</creator><general>Elsevier B.V</general><general>Elsevier</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7U5</scope><scope>8FD</scope><scope>L7M</scope></search><sort><creationdate>20100201</creationdate><title>Computation of invariant tori by Newton–Krylov methods in large-scale dissipative systems</title><author>Sánchez, J. ; Net, M. ; Simó, C.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c364t-51ec308a9e36b108b1eea8f0d87ef374218642394403488703ebef2f7e1df0083</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Continuation methods</topic><topic>Exact sciences and technology</topic><topic>Generalized Poincaré map</topic><topic>Invariant tori</topic><topic>Newton–Krylov methods</topic><topic>Physics</topic><topic>Resonances</topic><topic>Variational equations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Sánchez, J.</creatorcontrib><creatorcontrib>Net, M.</creatorcontrib><creatorcontrib>Simó, C.</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Physica. 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| language | eng |
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| source | Elsevier ScienceDirect Journals Complete |
| subjects | Continuation methods Exact sciences and technology Generalized Poincaré map Invariant tori Newton–Krylov methods Physics Resonances Variational equations |
| title | Computation of invariant tori by Newton–Krylov methods in large-scale dissipative systems |
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