Adaptative reduced order model to control non linear partial differential equations
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Estadístiques de LA Referencia / Recolecta
Inclou dades d'ús des de 2022
Cita com:
hdl:2117/190688
Tipus de documentText en actes de congrés
Data publicació2017
EditorCIMNE
Condicions d'accésAccés obert
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Abstract
In classical adjoint based optimal control of unsteady dynamical systems,
requirements of CPU time and storage memory are known to be very important. To
overcome this issue, model order reduction techiques operating by the construction of a separated
representation of the solution are considered. A spatial basis must be calcu- lated for each
variation in control parameters, followed by a Galerkin projection of the equations’s residuals on
this basis, that results in a low dimentional system of ordinary differential equations. These
steps need to be carried out in every iteration of the control algorithm. The most popular reduced
order model method is the Proper Orthogonal De- composition (POD). It is used here for the
construction of reduced bases. The interest in this communication is turned to the adaptation of
these bases respectivly to control parameter variations. Two adaptation approaches are considered.
The first one uses a powerfull interpolation method based on calculus of geodesic paths
on the Grassmann manifold. This approach needs a precomputed set of bases associated to a
distribution of opetating points, that are calculated using POD method. The second approach uses
the Proper Generalized Decomposition (PGD) considered here as a correction method. This method
consists in enriching a basis by reducing the error of the approximated solution.
ISBN978-84-946909-2-1
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Coupled-2017-73-Adaptative reduced order.pdf | 1,092Mb | Visualitza/Obre |