Comparison between the Discretized Continuous Gradient and the Discrete Gradient when Dealing with Nonlinear Parabolic Problems

REFERENCES

• O. Alifanov , Inverse Heat Conduction, Ill-Posed Problems , Wiley Interscience , New York , 1985 .
   Google Scholar
• D. N. Hào and H. J. Reinhardt , Stable Numerical Solution to Linear Inverse Heat Conduction Problems by the Conjugate Gradient Method , J. Inverse Ill-Posed Prob ., vol. 3 , pp. 447 – 467 , 1991 . [CSA]
   Google Scholar
• A. A. Tseng and F. Z. Zhao , Multidimensional Inverse Transient Heat Conduction Problems by Direct Sensitivity Coefficient Method Using a Finite-Element Scheme , Numer. Heat Transfer B , vol. 29 , pp. 365 – 380 , 1996 . [CSA]
   Web of Science ®Google Scholar
• Q. Bai and Y. Fujita , A Finite Element Analysis for Inverse Heat Conduction Problems—Japanese Research , Heat Transfer , vol. 6 , pp. 345 – 359 , 1997 . [CSA]
   Google Scholar
• R. Abou Khachfe and Y. Jarny , Determination of Heat Sources and Heat Transfer Coefficient for Two-Dimensional Heat Flow—Numerical and Experimental Study , Int. J. Heat Mass Transfer , vol. 44 , pp. 1309 – 1322 , 2001 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• K. A. Woodbury , Inverse Engineering Handbook , CRC Press , Boca Raton, Florida , 2002 .
   Google Scholar
• J. V. Beck , Inverse Heat Conduction. Ill-Posed Problems , Wiley/Interscience , New York , 1985 .
   Google Scholar
• D. Chenais and V. Lods , Comparaison du gradient discret et du gradient continu discrétisé dans le cadre de méthodes d'éléments finis non conformes , C. R. Acad. Sci., sér. 1, Mathématique , vol. 319 , pp. 493 – 498 , 1994 . [CSA]
   Google Scholar
• D. Chenais , Gradient discret et continu en optmisation de forme , Actes du colloque en l'honneur de Jean CEA, in Optimisation et contrôle , pp. 97 – 112 , Cépaduès , Toulouse , France , 1993 .
   Google Scholar
• S. H. Chung , L. Fourment , J. L. Chenot , and S. M. Hwang , Adjoint State Method for Shape Sensitivity Analysis in Non-steady Forming Applications , Int. J. Numer. Meth. Eng ., vol. 57 , pp. 1431 – 1444 , 2003 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• P. E. Gill , W. Murray , and M. H. Wright , Practical Optimization , Academic Press , London , UK , 1992 .
   Google Scholar
• M. Minoux , Mathematical Programming, Theory and Applications , Wiley , Chichester , UK , 1986 .
   Google Scholar
• Y. Favennec , V. Labbé , Y. Tillier , and F. Bay , Identification of Magnetic Parameters by Inverse Analysis Coupled with Finite-Element Modelling , IEEE Trans. Magn ., vol. 38 , no. 6 , pp. 3607 – 3619 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• O. M. Alifanov , Inverse Heat Transfer Problems , Springer-Verlag , Berlin , 1994 .
   Google Scholar
• Y. Jarny , M. N. Ozisik , and J. P. Bardon , A General Optimization Method Using Adjoint Equation for Solving Multidimensional Inverse Heat Conduction , Int. J. Heat Mass Transfer , vol. 34 , no. 11 , pp. 2911 – 2919 , 1991 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Y. Favennec , V. Labbé , and F. Bay , Induction Heating Processes Optimization—A General Optimal Control Approach , J. Comput. Phys ., vol. 187 , pp. 68 – 94 , 2003 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Y. Favennec , Optimization and Adjoint State , Thermal Measurements and Inverse Techniques—A Tool for the Characterization of Multiphysical Phenomena , in press , 2006 .
   Google Scholar
• O. C. Zienkiewicz , K. K. Morgan , and R. W. Lewis , Numerical Methods in Heat Transfer , Wiley , Chichester , UK , 1981 .
   Google Scholar
• A. Quarteroni and A. Valli , Numerical Approximation of Partial Differential Equations , Springer-Verlag , Berlin , 1994 .
   Google Scholar
• F. Bay , V. Labbé , Y. Favennec , and J. L. Chenot , A Numerical Model for Induction Heating Processes Coupling Electromagnetism and Thermomechanics , Int. J. Numer. Meth. Eng ., vol. 58 , no. 6 , pp. 839 – 867 , 2003 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• R. Abou Khachfe and Y. Jarny , Numerical Solution of 2-D Nonlinear Inverse Heat Conduction Problems Using Finite-Element Techniques, Numer. Heat Transfer B , vol. 37, pp. 45–67, 2000. [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• J. Su and G. F. Hewitt , Inverse Heat Conduction Problem of Estimating Time-Varying Heat Transfer Coefficient , Numer. Heat Transfer A , vol. 45 , pp. 777 – 789 , 2004 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• A. Anju and M. Kawahara , Comparison of Sensitivity Equation and Adjoint Equation Methods for Parameter Identification Problems , Int. J. Numer. Meth. Eng ., vol. 40 , pp. 1015 – 1024 , 1997 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• F. Beux , Un algorithme d'optimisation d'une forme aérodynamique par une méthode de gradient exact , in Optimisation et Contrôle, Actes du colloque organisé en l'honneur du soixantième anniversaire de Jean Céa , Cépaduès , Toulouse , France , 1993 .
   Google Scholar
• A. Ghouali , S. Ortola , A. Oster , and G. Duvaut , Local Analytical Sensitivity Analysis for the Forging Gamut Optimization , in Ecole Centrate de Nantes Ed., Nantes IDMME 96 , pp. 985 – 994 , 1996 .
   Google Scholar
• S. H. Chung , L. Fourment , J. L. Chenot , and S. M. Hwang , Adjoint State Method for Shape Sensitivity Analysis in Non-steady Forming Applications , Int. J. Numer. Meth. Eng ., vol. 57 , no. 10 , pp. 1431 – 1444 , 2003 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• O. Bodart , A. V. Boureau , and R. Touzani , Numerical Investigation of Optimal Control of Induction Heating Processes , Appl. Math. Modell ., no. 25 , pp. 697 – 712 , 2001 . [CSA]
   Google Scholar
• Y. Favennec , V. Labbé , and F. Bay , The Ultraweak Time Coupling in Nonlinear Multiphysics Modeling & Related Optimization Problems , Int. J. Numer. Meth. Eng ., vol. 60 , no. 4 , pp. 803 – 831 , 2004 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• K. Eriksson and C. Johnson , Error Estimates and Automatic Time Step Control for Nonlinear Parabolic Problems , SIAM J. Numer. Anal ., no. 24 , pp. 12 – 23 , 1987 . [CSA] [CROSSREF]
   Google Scholar
• E. Videcoq and D. Petit , Model Reduction for the Resolution of Multidimensional Inverse Heat Conduction Problems , Int. J. Heat Mass Transfer , vol. 44 , no. 10 , pp. 1899 – 1911 , 2001 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar