A Lie-Group Adaptive Method to Identify Spatial-Dependence Heat Conductivity Coefficients

Abstract

We consider an inverse problem for numerically estimating a spatial-dependence heat conductivity α(x) in T _t (x, t) = ∂[α(x)T _x ]/∂ x + h(x, t), 0 < t < t _f , 0 < x < ℓ; α(x) is assumed to be a continuous function of x, and α(ℓ) is given. An iterative Lie-group adaptive method (LGAM) is developed, which can be used to find α(x) at the spatially discretized locations x _i , requiring only a few measured temperature data at a final time t _f as a target to select a suitable value of the parameter r ∈ [0, 1] appearing in the present method. The new method has three advantages in that no a priori information of the heat conductivity function is required, only a few extra data are measured, and it is robust againt noise. The accuracy and efficiency of the present method are confirmed by comparing the estimated results with some exact solutions.

Acknowledgments

Taiwan's National Science Council Project NSC-99-2221-E-002-074-MY3, granted to the author, is highly appreciated.