Open Access

ARTICLE

An LGEM to Identify Time-Dependent Heat Conductivity Function by an Extra Measurement of Temperature Gradient

Chein-Shan Liu^1,2

1 Department of Mechanical and Mechatronic Engineering,Taiwan Ocean University, Keelung, Taiwan
2 Department of Harbor and River Engineering, Tai-wan Ocean University, Keelung, Taiwan.E-mail: csliu@mail.ntou.edu.tw

Computers, Materials & Continua 2008, 7(2), 81-96. https://doi.org/10.3970/cmc.2008.007.081

Abstract

We consider an inverse problem for estimating an unknown heat conductivity parameter α(t) in a heat conduction equation T_t(x,t) = α(t)T_xx(x,t) with the aid of an extra measurement of temperature gradient on boundary. Basing on an establishment of the one-step Lie-group elements G(r) and G(l) for the semi-discretization of heat conduction equation in time domain, we can derive algebraic equations from G(r) = G(l). The new method, namely the Lie-group estimation method (LGEM), is examined through numerical examples to convince that it is highly accurate and efficient; the maximum estimation error is smaller than 10^-5 for smooth parameter and for discontinuous and oscillatory parameter the accuracy is still in the order of 10^-2. Although the estimation is carried out under a large measurement noise, the LGEM is also stable.

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Keywords

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