NDLI: Estimation of constant thermal conductivity by use of Proper Orthogonal Decomposition

Content Provider	Springer Nature Link
Author	Ostrowski, Ziemowit Białecki, Ryszard A. Kassab, Alain J.
Copyright Year	2005
Abstract	An inverse approach is developed to estimate the unknown heat conductivity and the convective heat transfer coefficient. The method relies on proper orthogonal decomposition (POD) in order to filter out the higher frequency error. The idea is to solve a sequence of direct problems within the body under consideration. The solution of each problem is sampled at a predefined set of points. Each sampled temperature field, known in POD parlance as a snapshot, is obtained for an assumed value of the retrieved parameters. POD analysis, as an efficient mean of detecting correlation between the snapshots, yields a small set of orthogonal vectors (POD basis), constituting an optimal set of approximation functions. The temperature field is then expressed as a linear combination of the POD vectors. In standard applications, the coefficients of this combination are assumed to be constant. In the proposed approach, the coefficients are allowed to be a nonlinear function of the retrieved parameters. The result is a trained POD base, which is then used in inverse analysis, resorting to a condition of minimization of the discrepancy between the measured temperatures and values calculated from the model. Several numerical examples show the robustness and numerical stability of the scheme.
Starting Page	52
Ending Page	59
Page Count	8
File Format	PDF
ISSN	01787675
Journal	Computational Mechanics
Volume Number	37
Issue Number	1
e-ISSN	14320924
Language	English
Publisher	Springer-Verlag
Publisher Date	2005-06-04
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Inverse problems Proper Orthogonal Decomposition Regularization Heat transfer Heat conductivity Thermodynamics Condensed Matter Numerical and Computational Methods in Engineering Systems and Information Theory in Engineering Theoretical and Applied Mechanics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Ocean Engineering Computational Theory and Mathematics Mechanical Engineering Computational Mechanics Computational Mathematics

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