A parallel algorithm for the computation of invariant tori in large-scale dissipative systems

A parallelizable algorithm to compute invariant tori of high-dimensional dissipative systems, obtained upon discretization of PDEs is presented. The size of the set of equations to be solved is only a small multiple of the dimension of the original system. The sequential and parallel implementations...

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Vydáno v:Physica. D Ročník 252; s. 22 - 33
Hlavní autoři: Sánchez, J., Net, M.
Médium: Journal Article Publikace
Jazyk:angličtina
Vydáno: Elsevier B.V 01.06.2013
Témata:
Algorismes paral·lels
Continuation methods
Física
Generalized Poincaré maps
Invariant tori
Mètodes de continuació
Newton–Krylov methods
Parallel algorithms
Variational equations
Àrees temàtiques de la UPC
Newton–Krylov methods
Variational equations
Generalized Poincaré maps
Invariant tori
Parallel algorithms
Continuation methods
ISSN:0167-2789, 1872-8022
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Shrnutí:A parallelizable algorithm to compute invariant tori of high-dimensional dissipative systems, obtained upon discretization of PDEs is presented. The size of the set of equations to be solved is only a small multiple of the dimension of the original system. The sequential and parallel implementations are compared with a previous method (Sánchez et al. (2010)) [11], showing that important savings in wall-clock time can be achieved. In order to test it, a thermal convection problem of a binary mixture of fluids has been used. The new method can also be applied to problems with very low rotation numbers, for which the previous is not suitable. This is tested in two examples of two-dimensional maps. •A parallel algorithm to compute invariant tori of large-scale 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.•Speed-ups around the number of processors employed are achieved for the new method.•The comparison with the old method shows speed-ups above the number of processors.
ISSN:0167-2789
1872-8022
DOI:10.1016/j.physd.2013.02.008