#### Title

Estimation of constant thermal conductivity by use of Proper Orthogonal Decomposition

#### Abbreviated Journal Title

Comput. Mech.

#### Keywords

inverse problems; Proper Orthogonal; decomposition; regularization; heat; transfer; heat conductivity; EQUATIONS; Mathematics, Interdisciplinary Applications; Mechanics

#### 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.

#### Journal Title

Computational Mechanics

#### Volume

37

#### Issue/Number

1

#### Publication Date

1-1-2005

#### Document Type

Article; Proceedings Paper

#### Language

English

#### First Page

52

#### Last Page

59

#### WOS Identifier

#### ISSN

0178-7675

#### Recommended Citation

"Estimation of constant thermal conductivity by use of Proper Orthogonal Decomposition" (2005). *Faculty Bibliography 2000s*. 5526.

https://stars.library.ucf.edu/facultybib2000/5526

## Comments

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