A Green's function numerical method for some inverse boundary value problems

References

• Bryan , K. 1993 . “An Inverse Problem in Thermal Imaging,” Computation and Control III, Bozeman, MT ” . In Progress in Systems and Control Theory , Vol. 15 , 73 – 82 . Boston, MA : Birkhauser .
   Google Scholar
• Brian , K. and Vogelius , M. 1992 . “A Uniqueness Result Concerning the Identification of a Collection of Cracks from Finitely Many Electrostatic Boundary Measurements,” . SIAM Journal of Mathematical Analysis , 23 ( 4 ) July : 950 – 958 .
   Google Scholar
• Das , S. and Mitra , A.K. 1992 . “An Algorithm for the Solution of Inverse Laplace Problems and its Application in Flaw Identification in Materials,” . Journal of Computational Physics , 99 : 99 – 105 .
   Web of Science ®Google Scholar
• Friedman , A. and Vogelius , M. 1989 . “Determining Cracks by Boundary Measurements,” . Indiana University Mathematics Journal , 38 : 527 – 556 .
   Web of Science ®Google Scholar
• Henrici , P. 1986 . Applied and Computational Complex Analysis , Vol. 3 , New York, London : Wiley .
   Google Scholar
• Isakov , V. 1998 . Inverse Problems for Partial Differential Equations , Applied Mathematical Sciences 127 New York & Berlin : Springer .
   Google Scholar
• Kassab , A.J. , Hsieh , C.K. and Pollard , J. 1997 . “Solution of the Inverse Geometric Problem for the Detection of Subsurface Cavities by the IR‐CAT Method,” . In Boundary Integral Formulations for Inverse Analysis , Edited by: Ingham , D.B. and Wrobel , L. C. 33 – 66 . Southampton : Computational Mechanics Publications .
   Google Scholar
• Marquardt , D.W. 1963 . “An Algorithm for Least‐squares Wstimation of Nonlinear Parameters,” . Journal of the Society of Industrial and Applied Mathematicians , 11 : 431 – 441 .
   Web of Science ®Google Scholar
• Melnikov , Yu. A. 1977 . “Some Applications of the Green's Function Method in Mechanics,” . International Journal of Solids and Structures , 13 : 1045 – 1058 .
   Google Scholar
• Melnikov , Yu. A. 1995 . Green's Functions in Applied Mechanics , Southampton : Computational Mechanics Publications .
   Google Scholar
• Melnikov , Yu. A. and Koshnarjova , V.A. 1994 . “Green's Matrices and 2‐D Elasto‐potentials for External Boundary Value Problems,” . Applied Mathematical Modelling , 18 : 161 – 167 .
   Google Scholar
• Melnikov , Yu. A. and Powell , J.O. 1998 . “Green's Functions in the Numerical Solution of Some Inverse Boundary Value Problems,” . In Boundary Elements XX , 351 – 361 . Southampton : Computational Mechanics Publications .
   Google Scholar
• Melnikov , Yu. A. and Titarenko , S.A. 1995 . “Green's Function BEM for 2‐D Optimal Shape Design,” . Engineering Analysis with Boundary Elements , 15 : 1 – 10 .
   Google Scholar
• Miranda , C. 1970 . Partial Differential Equations of Elliptic Type , Ergenbisse der Math. und ihrer Grenzgebiete Vol. Bd. 2 , New York‐Berlin : Springer . MR 44 /# 1924
   Google Scholar
• Muskhelishvili , N.I. 1992 . Singular Integral Equations , New York : Dover Publications, Inc. .
   Google Scholar
• Oguz , H.N. and Han , D. 1998 . “3‐D Impedance Tomography of High Contrast Objects,” . In Boundary Elements XX , 361 – 371 . Southampton : Computational Mechanics Publications .
   Google Scholar
• Saigal , S. and Zeng , X. 1992 . “An Inverse Formulation with Boundary Elements,” . Journal of Applied Mechanics , 59 : 835 – 840 .
   Google Scholar
• Schnur , D. and Zabaras , N. 1992 . “An Inverse Method for Determining Elastic Material Properties and a Material Interface,” . International Journal of Numerical Methods in Engineering , 33 : 2039 – 2057 .
   Web of Science ®Google Scholar
• Sylvester , J. and Uhlmann , G. 1987 . “A global Uniqueness Theorem for an Inverse Boundary Value Problem,” . Annals of Mathematics , 125 : 153 – 169 .
   Web of Science ®Google Scholar
• Tanaka , M. and Masuda , Y. 1986 . “Boundary Element Method Applied to Some Inverse Problems,” . Engineering Analysis , 3 : 138 – 143 .
   Google Scholar
• Correspondence addressee
   Google Scholar