9,616 research outputs found
Anomalous dissipation in a stochastic inviscid dyadic model
A stochastic version of an inviscid dyadic model of turbulence, with
multiplicative noise, is proved to exhibit energy dissipation in spite of the
formal energy conservation. As a consequence, global regular solutions cannot
exist. After some reductions, the main tool is the escape bahavior at infinity
of a certain birth and death process.Comment: Published in at http://dx.doi.org/10.1214/11-AAP768 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Inexact Solves in Interpolatory Model Reduction
We investigate the use of inexact solves for interpolatory model reduction
and consider associated perturbation effects on the underlying model reduction
problem. We give bounds on system perturbations induced by inexact solves and
relate this to termination criteria for iterative solution methods. We show
that when a Petrov-Galerkin framework is employed for the inexact solves, the
associated reduced order model is an exact interpolatory model for a nearby
full-order system; thus demonstrating backward stability. We also give evidence
that for \h2-optimal interpolation points, interpolatory model reduction is
robust with respect to perturbations due to inexact solves. Finally, we
demonstrate the effecitveness of direct use of inexact solves in optimal
approximation. The result is an effective model reduction
strategy that is applicable in realistically large-scale settings.Comment: 42 pages, 5 figure
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