Using a Lie-Group Adaptive Method for the Identification of a Nonhomogeneous Conductivity Function and Unknown Boundary Data
Chein-Shan Liu

Source CMC: Computers, Materials & Continua, Vol. 21, No. 1, pp. 17-40, 2011
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Keywords Inverse problem, Mixed-type inverse problem, Parameter identification, Inverse heat conduction problem, Lie-group adaptive method, Spatial-dependence heat conductivity
Abstract Only the left-boundary data of temperature and heat flux are used to estimate an unknown parameter function a(x) in Tt(x,t)=(a(x)Tx)/x+h(x,t), as well as to recover the right-boundary data. When a(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 a(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 a(x) through a few iterations. To test the stability of the present LGAM we also add a random noise in the initial data. When a(x) is identified, a sideways approach is employed to recover the unknown boundary data. The convergence speed and accuracy are examined by numerical examples.
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