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Descripción
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| Proper orthogonal decomposition (POD) is a very e ective means to identify dynamical information contained in sets of snapshots that cover numerically computed trajectories of dissipative systems of partial di erential equations. Such information is organized in a hierarchy of POD modes and the system can be Galerkin-projected onto the associated linear subspace. Quite frequently, the outcome is a low dimensional model of the problem. Flexibility and e?ciency of the approximation can be enhanced if POD is applied `on the y', adaptively combining a standard numerical solver (which provides the necessary snapshots) with the reduced system in interspersed intervals, as both time and a bifurcation parameter are varied. Residual estimates are introduced to make this adaptation accurate and robust, preventing possible mode truncation instabilities in the presence of complex dynamics. All ideas are illustrated in some bifurcation scenarios including quasi-periodic and chaotic attractors, which highlights a good computational e?ciency. | |
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Internacional
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JCR del ISI
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Título de la revista
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Dynamical systems, differential equations, and applications |
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ISSN
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00000000 |
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Factor de impacto JCR
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Información de impacto
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Volumen
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DOI
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10.3934/proc.2015.1060 |
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Número de revista
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Desde la página
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1060 |
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Hasta la página
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1069 |
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Mes
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SIN MES |
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Ranking
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