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| - Optimal Field Reconstruction of Distributed Process Systems from PartialMeasurements
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| Abstract
| - In this article, we develop a systematic approach for efficient field reconstruction in distributed process systemsfrom a limited number of measurements. The approach generalizes previous methods for sensor placementso as to be able to handle field reconstruction problems in arbitrary spatial domains where complex nonlinearphenomena take place. Pattern formation in fluid dynamics or diffusion-reaction systems are examples exhibitingcomplex nonlinear distributed behaviors, especially when taking place in arbitrary 2D or 3D domains. Ourapproach exploits the dissipative nature of the diffusion-convection process and the underlying algebraicstructure of the finite element method to efficiently construct field representations in terms of globally definedbasis functions and to optimally select the placement of sensors. The results will be illustrated on a fluiddynamic process: the Rayleigh−Bénard problem.
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