@Article{cmc.2011.021.017,
AUTHOR = {Chein-Shan Liu},
TITLE = {Using a Lie-Group Adaptive Method for the Identification of a Nonhomogeneous Conductivity Function and Unknown Boundary Data},
JOURNAL = {Computers, Materials \& Continua},
VOLUME = {21},
YEAR = {2011},
NUMBER = {1},
PAGES = {17--40},
URL = {http://www.techscience.com/cmc/v21n1/22601},
ISSN = {1546-2226},
ABSTRACT = {Only the left-boundary data of temperature and heat flux are used to estimate an unknown parameter function α(x) in T<sub>t</sub>(x,t) = ∂(α(x)T<sub>x</sub>)/∂x + h(x,t), as well as to recover the right-boundary data. When α(x) is given the above problem is a well-known inverse heat conduction problem (IHCP). This paper solves a mixed-type inverse problem as a combination of the IHCP and the problem of parameter identification, without needing to assume a function form of α(x) a priori, and without measuring extra data as those used by other methods. We use the one-step Lie-Group Adaptive Method (LGAM) for the semi-discretizations of heat conduction equation, respectively, in time domain and spatial domain to derive algebraic equations, which are used to solve α(x) through a few iterations. To test the stability of the present LGAM we also add a random noise in the initial data. When α(x) is identified, a sideways approach is employed to recover the unknown boundary data. The convergence speed and accuracy are examined by numerical examples.},
DOI = {10.3970/cmc.2011.021.017}
}