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

REFERENCES

• G. P. Flash and N. M. Özisik , Inverse Heat Conduction Problem of Simultaneously Estimating Spatially Varying Thermal Conductivity and Heat Capacity per Unit Volume , Numer. Heat Transfer A , vol. 16 , pp. 249 – 266 , 1989 .
   Google Scholar
• W. K. Yeung and T. T. Lam , Second-Order Finite Difference Approximation for Inverse Determination of Thermal Conductivity , Int. J. Heat Mass Transfer , vol. 39 , pp. 3685 – 3693 , 1996 .
   Web of Science ®Google Scholar
• Y. L. Keung and J. Zou , Numerical Identifications of Parameters in Parabolic Systems , Inverse Probl. , vol. 14 , pp. 83 – 100 , 1998 .
   Web of Science ®Google Scholar
• J. H. Lin , C. K. Chen , and Y. T. Yang , Inverse Method for Estimating Thermal Conductivity in One-Dimensional Heat Conduction Problems , J. Thermophys. Heat Transfer , vol. 15 , pp. 34 – 41 , 2001 .
   Web of Science ®Google Scholar
• C. L. Chang and M. Chang , Non-Iteration Estimation of Thermal Conductivity Using Finite Volume Method , Int. Commun. Heat Mass Transfer , vol. 33 , pp. 1013 – 1020 , 2006 .
   Web of Science ®Google Scholar
• C. Jia and G. Wang , Identifications of Parameters in Ill-Posed Linear Parabolic Equations , Nonlinear Anal. , vol. 57 , pp. 677 – 686 , 2004 .
   Web of Science ®Google Scholar
• C.-S. Liu , L. W. Liu , and H. K. Hong , Highly Accurate Computation of Spatial-Dependent Heat Conductivity and Heat Capacity in Inverse Thermal Problem , CMES: Comput. Model. Eng. Sci. , vol. 17 , pp. 1 – 18 , 2007 .
   Web of Science ®Google Scholar
• C.-S. Liu , An LGSM to Identify Nonhomogeneous Heat Conductivity Functions by an Extra Measurement of Temperature , Int. J. Heat Mass Transfer , vol. 51 , pp. 2603 – 2613 , 2008 .
   Web of Science ®Google Scholar
• Q. Chen and J. Liu , Solving an Inverse Parabolic Problem by Optimization from Final Measurement Data, J. Comput. Appl. Math. , vol. 193, pp. 183–203, 2006.
   Web of Science ®Google Scholar
• H. W. Engl and J. Zou , A New Approach to Convergence Rate Analysis of Tikhonov Regularization for Parameter Identification in Heat Conduction , Inverse Probl. , vol. 16 , pp. 1907 – 1923 , 2000 .
   Web of Science ®Google Scholar
• E. Divo , A. Kassab , and F. Rodriguez , Characterization of Space Dependent Thermal Conductivity with a BEM-Based Genetic Algorithm , Numer. Heat Transfer A , vol. 37 , pp. 845 – 875 , 2000 .
   Web of Science ®Google Scholar
• C. H. Huang and N. M. Özisik , Direct Integration Approach for Simultaneously Estimating Temperature Dependent Thermal Conductivity and Heat Capacity , Numer. Heat Transfer A , vol. 20 , pp. 95 – 110 , 1991 .
   Web of Science ®Google Scholar
• K. C. Liu and C. T. Lin , Solution of an Inverse Heat Conduction Problem in a Bi-layered Spherical Tissue , Numer. Heat Transfer A , vol. 58 , pp. 802 – 818 , 2010 .
   Web of Science ®Google Scholar
• S. K. Kim , Resolving the Final Singularity in Gradient Methods for Inverse Heat Conduction Problems , Numer. Heat Transfer B , vol. 57 , pp. 74 – 88 , 2010 .
   Web of Science ®Google Scholar
• S. Vakali and M. S. Gadala , Effectiveness and Efficiency of Particle Swarm Optimization Technique in Inverse Heat Conduction Analysis , Numer. Heat Transfer B , vol. 56 , pp. 119 – 141 , 2009 .
   Web of Science ®Google Scholar
• M. Samai and T. Loulou , A Comparative Study of Heat Flux and Temperature Based Objective Functional to Solve Inverse Heat Conduction Problems , Numer. Heat Transfer B , vol. 56 , pp. 75 – 104 , 2009 .
   Web of Science ®Google Scholar
• H. Molavi , I. Pourshaban , A. Hakkaki-Fard , M. Molavi , A. Ayasoufi , and R. K. Rahmani , Inverse Identification of Thermal Properties of Charring Ablators , Numer. Heat Transfer B , vol. 56 , pp. 478 – 501 , 2009 .
   Web of Science ®Google Scholar
• M. J. Kazemzadeh-Parsi and F. Daneshmand , Cavity-Shape Identification with Convective Boundary Conditions Using Non-Boundary-Fitted Meshes , Numer. Heat Transfer B , vol. 57 , pp. 283 – 305 , 2010 .
   Web of Science ®Google Scholar
• C. P. Naveira-Cotta , H. R. B. Orlande , and R. M. Cotta , Integral Transforms and Bayesian Inference in the Identification of Variable Thermal Conductivity in Two-Phase Dispersed Systems , Numer. Heat Transfer B , vol. 57 , pp. 173 – 202 , 2010 .
   Web of Science ®Google Scholar
• J. Y. Tan , J. M. Zhao , and L. H. Liu , Meshless Method for Geometry Boundary Identification Problem of Heat Conduction , Numer. Heat Transfer B , vol. 55 , pp. 135 – 154 , 2009 .
   Web of Science ®Google Scholar
• D. Slota , Identification of the Cooling Condition in 2-D and 3-D Continuous Casting Processes , Numer. Heat Transfer B , vol. 55 , pp. 155 – 176 , 2009 .
   Web of Science ®Google Scholar
• C. M. Fan and H. F. Chan , Modified Collocation Trefftz Method for the Geometry Boundary Identification Problem of Heat Conduction , Numer. Heat Transfer B , vol. 59 , pp. 58 – 75 , 2011 .
   Web of Science ®Google Scholar
• T. T. Lam and W. K. Yeung , Inverse Determination of Thermal Conductivity for One-Dimensional Problems , J. Thermophys. Heat Transfer , vol. 9 , pp. 335 – 344 , 1995 .
   Web of Science ®Google Scholar
• C.-S. Liu , Cone of Non-Linear Dynamical System and Group Preserving Schemes , Int. J. Non-Linear Mech. , vol. 36 , pp. 1047 – 1068 , 2001 .
   Web of Science ®Google Scholar
• C.-S. Liu , The Lie-Group Shooting Method for Nonlinear Two-Point Boundary Value Problems Exhibiting Multiple Solutions , CMES: Comput. Model. Eng. Sci. , vol. 13 , pp. 149 – 163 , 2006 .
   Web of Science ®Google Scholar
• C.-S. Liu , One-Step GPS for the Estimation of Temperature-Dependent Thermal Conductivity , Int. J. Heat Mass Transfer , vol. 49 , pp. 3084 – 3093 , 2006 .
   Web of Science ®Google Scholar
• C.-S. Liu , An Efficient Simultaneous Estimation of Temperature-Dependent Thermophysical Properties , CMES: Comput. Model. Eng. Sci. , vol. 14 , pp. 77 – 90 , 2006 .
   Web of Science ®Google Scholar
• C.-S. Liu , Identification of Temperature-Dependent Thermophysical Properties in a Partial Differential Equation Subject to Extra Final Measurement Data , Numer. Meth. Partial Diff. Eq. , vol. 23 , pp. 1083 – 1109 , 2007 .
   Web of Science ®Google Scholar
• C.-S. Liu , Nonstandard Group-Preserving Schemes for Very Stiff Ordinary Differential Equations, CMES: Comput. Model. Eng. Sci. , vol. 9, pp. 255–272, 2005.
   Web of Science ®Google Scholar
• C.-S. Liu and S. N. Atluri , An Iterative and Adaptive Lie-Group Method for Solving the Caldero′n Inverse Problem , CMES: Comput. Model. Eng. Sci. , vol. 64 , pp. 299 – 326 , 2010 .
   Web of Science ®Google Scholar
• C.-S. Liu , A Lie-Group Adaptive Method for Imaging a Space-Dependent Rigidity Coefficient in an Inverse Scattering Problem of Wave Propagation , CMC: Comput. Mater. Continua , vol. 18 , pp. 1 – 21 , 2010 .
   Web of Science ®Google Scholar
• C.-S. Liu , A Self-Adaptive LGSM to Recover Initial Condition or Heat Source of One-Dimensional Heat Conduction Equation by Using Only Minimal Boundary Thermal Data , Int. J. Heat Mass Transfer , vol. 54 , pp. 1305 – 1312 , 2011 .
   Web of Science ®Google Scholar
• C.-S. Liu , Using a Lie-Group Adaptive Method for the Identification of a Nonhomogeneous Conductivity Function and Unknown Boundary Data , CMC: Comput. Mater. Continua , vol. 21 , pp. 17 – 39 , 2011 .
   Web of Science ®Google Scholar