Adjoint-weighted variational formulation for a direct computational solution of an inverse heat conduction problem

Inverse Problems

Volumn 23, Issue 6, 2007, Pages 2325-2342

  Barbone, Paul E ^a   Oberai, Assad A ^a,b   Harari, Isaac ^a,c  

^a BOSTON UNIVERSITY   (United States)

^b RENSSELAER POLYTECHNIC INSTITUTE   (United States)

^c TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL METHODS; CONVERGENCE OF NUMERICAL METHODS; INVERSE PROBLEMS; PROBLEM SOLVING; TEMPERATURE DISTRIBUTION; THERMAL CONDUCTIVITY;

ADVECTIVE TRANSPORT; VARIATIONAL FORMULATION;

HEAT CONDUCTION;

EID: 36749087742     PISSN: 02665611     EISSN: 13616420     Source Type: Journal    
DOI: 10.1088/0266-5611/23/6/003     Document Type: Article

References (36)

1. Richter G R 1981 Math. Comput. 36 375-86
2. Richter G R 1981 SIAM J. Appl. Math. 41 210-21
3. Falk R S 1983 Math. Comput. 40 537-46
4. Knowles I and Wallace R 1996 Inverse Problems 12 953-63
5. Surana K S and Huels R C 1989 Comput. Struct. 31 249-68
6. Acar R 1993 SIAM J. Control Optim. 31 1221-44
7. Alcolea A, Carrera J and Medina A 2006 Adv. Water Resour. 29 1678-89
8. Reeve D E and Spivack M 1994 Inverse Problems 10 1335-44
9. Spivack M and Reeve D E 1999 J. Comput. Phys. 151 585-96
10. Spivack M and Reeve D E 2000 J. Comput. Phys. 161 169-81
11. Lee J Y 2004 Inverse Problems 20 847-58
12. Plewes D B and Cheng H L M 2002 J. Magn. Reson. Imaging 16 598-609
13. Parker D L, Smith V, Sheldon P, Crooks L E and Fussell L 1983 Med. Phys. 10 321-5
14. Miller N R, Bamber J C and ter Haar G R 2004 Ultrasound Med. Biol. 30 345-56
15. Leutz W and Maret G 1995 Physica B 204 14-9
16. Muthupillai R, Lomas D J, Rossman P J, Greenleaf J F, Manduca A and Ehman R L 1995 Science 269 1854-7
17. Ophir J, Cespedes I, Ponnekanti H, Yazdi Y and Li X 1991 Ultrason. Imaging 13 111-34
18. Barbone P E and Bamber J 2002 Phys. Med. Biol. 47 2147-64
19. Barbone P E and Gokhale N 2004 Inverse Problems 20 283-96
20. Oberai A, Gokhale N and Feijoo G 2003 Inverse Problems 19 297-313
21. Oberai A A, Gokhale N H, Doyley M M and Bamber J C 2004 Phys. Med. Biol. 49 2955-74
22. Manduca A, Oliphant T, Dresner M, Mahowald J, Kruse S, Amromin E, Felmlee J, Greenleaf J and Ehman R 2001 Med. Image Anal. 5 237-54
23. Oliphant T, Manduca A, Ehman R and Greenleaf J 2001 Magn. Reson. Med. 45 299-310
24. Ji L, McLaughlin J R, Renzi D and Yoon J R 2003 Inverse Problems 19 S1-S29
25. Ji L and McLaughlin J 2004 Inverse Problems 20 1-24
26. Knowles I 1999 SIAM J. Appl. Math. 59 1356-70
27. Oberai A A, Barbone P E and Harari I 2007 Int. J. Numer. Methods Fluids 54 683-93
28. Oden J T and Demkowicz L F 1996 Applied Functional Analysis (CRC Series in Computational Mechanics and Applied Analysis) (Boca Raton, FL: CRC Press) ISBN 0-8493-2551-X
29. Franca L P, Hauke G and Masud A 2006 Comput. Methods Appl. Mech. Eng. 195 1560-72
30. Bochev P B and Choi J 2001 Comput. Methods Appl. Math. 1 115-24
31. Barbone P E and Harari I 2001 Comput. Methods Appl. Mech. Eng. 190 5679-90
32. Reddy B D 1998 Introductory Functional Analysis (New York: Springer)
33. Brenner S C and Scott L R 2002 The Mathematical Theory of Finite Element Methods (New York: Springer)
34. Kantorovich L and Akilov G 1964 Functional Analysis in Normed Spaces ed D E Brown transl. (New York: Pergamon)
35. Acosta G and Durn R G 2004 Proc. Am. Math. Soc. 132 195-202
36. Payne L E and Weinberger H F 1960 Arch. Ration. Mech. Anal. 5 286-92