TY - EJOU
AU - Liu, Chein-Shan
TI - An LGEM to Identify Time-Dependent Heat Conductivity Function by an Extra Measurement of Temperature Gradient
T2 - Computers, Materials \& Continua
PY - 2008
VL - 7
IS - 2
SN - 1546-2226
AB - We consider an inverse problem for estimating an unknown heat conductivity parameter α(t) in a heat conduction equation Tt(x,t) = α(t)Txx(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.
KW - Inverse problem
KW - Parameter identification
KW - Lie-group estimation method
KW - Time-dependent heat conductivity
DO - 10.3970/cmc.2008.007.081