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On the multiple shooting continuation of periodic orbits by NewtonKrylov methods
 Int. J.Bifurcation and Chaos
, 2010
"... The application of the multiple shooting method to the continuation of periodic orbits in largescale dissipative systems is analyzed. A preconditioner for the linear systems which appear in the application of Newton’s method is presented. It is based on the knowledge of invariant subspaces of the J ..."
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The application of the multiple shooting method to the continuation of periodic orbits in largescale dissipative systems is analyzed. A preconditioner for the linear systems which appear in the application of Newton’s method is presented. It is based on the knowledge of invariant subspaces of the Jacobians at nearby solutions. The possibility of speeding up the process by using parallelism is studied for the thermal convection of a binary mixture of fluids in a rectangular domain, with positive results.
Computation of invariant tori by NewtonKrylov methods in
"... largescale dissipative systems. ..."
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5 National Centre for Engineering Systems of Complex Fluids, University Politehnica of
, 2013
"... Abstract. We provide an overview of current techniques and typical applications of numerical bifurcation analysis in fluid dynamical problems. Many of these problems are characterized by highdimensional dynamical systems which undergo transitions as parameters are changed. The computation of the cr ..."
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Abstract. We provide an overview of current techniques and typical applications of numerical bifurcation analysis in fluid dynamical problems. Many of these problems are characterized by highdimensional dynamical systems which undergo transitions as parameters are changed. The computation of the critical conditions associated with
Invariant tori Parallel algorithms Continuation methods Generalized Poincaré maps
, 2013
"... ih i g h l i g h t s • A parallel algorithm to compute invariant tori of largescale systems is presented. • The new method is compared with a previous serial algorithm. • The two methods are applied to the thermal convection of a binary mixture. • Speedups around the number of processors employed ..."
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ih i g h l i g h t s • A parallel algorithm to compute invariant tori of largescale systems is presented. • The new method is compared with a previous serial algorithm. • The two methods are applied to the thermal convection of a binary mixture. • Speedups around the number of processors employed are achieved for the new method. • The comparison with the old method shows speedups above the number of processors. a r t i c l e i n f o Article history: