A reduced-order approach for optimal control of fluids using proper orthogonal decomposition

By S. S. Ravindran. 2000

440 citations recorded by the source corpus.

Subfields: Computational Mechanics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b820fe229bb0c4592459b970b56ea60d7d02f50c

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In Computational Mechanics

In Statistical and Nonlinear Physics

Citations in the corpus

A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations (2005, neutral): “, of the variety described above) are often employed: applications range from fluid flow [16–18, 36] to hyperthermia treatment [24, 25] to thermal processing of semiconductors [30] and canned foods [4].”
Model Order Reduction in Fluid Dynamics: Challenges and Perspectives (2014, background): “Ad hoc reduced order modelling techniques have recently been proposed for optimal flow control problems [104, 108, 121], optimal shape design of devices related with fluid flows [6, 58, 23, 88], and the treatment of fluid-structure interaction problems [76, 78].”
A robust multi-model predictive controller for distributed parameter systems (2012, background): “Each element φi(ξ) of the set of basis functions is computed off-line as the solution of the following integral eigenvalue problem [38, 63, 66]: λi ∫”
An efficient reduced‐order modeling approach for non‐linear parametrized partial differential equations (2008, background): “Nevertheless, its success and thus applications remain very much limited to linear and quadratically non-linear problems such as linearized Euler and parabolic equations [12, 13, 23], Burgers equation [10, 24], and incompressible Navier– Stokes equations [11, 25, 26].”
Using Bayesian statistics in the estimation of heat source in radiation (2005, methodology): “One widely used approach of model-reduction is the computation of the proper orthogonal decomposition (POD) basis using the method of snapshots [26, 27].”
Nonlinear Model Reduction via Discrete Empirical Interpolation (2010, background): “However, effective dimension reduction for the POD-Galerkin approach is usually limited to problems with linear or bilinear terms as in [20, 22, 18, 33].”