On the fréchet derivative for obstacle scattering with an impedance boundary condition

SIAM Journal on Applied Mathematics

Volumn 65, Issue 1, 2005, Pages 194-208

  Haddar, Houssem ^a   Kress, Rainer ^b  

^a INRIA ROCQUENCOURT   (France)

^b UNIVERSITY OF GÖTTINGEN   (Germany)

Author keywords

Acoustic scattering; Electromagnetic scattering; Far field pattern; Fr chet derivative; Helmholtz equation; Impedance condition; Inverse scattering; Maxwell equations; Obstacle scattering

Indexed keywords

ACOUSTICS; BOUNDARY CONDITIONS; INTEGRAL EQUATIONS; ITERATIVE METHODS; MAXWELL EQUATIONS; PROBLEM SOLVING;

ACOUSTIC SCATTERING; ELECTROMAGNETIC SCATTERING; FAR FIELD PATTERN; FRÉCHET DERIVATIVES; HELMHOLTZ EQUATION; IMPEDANCE CONDITIONS; INVERSE SCATTERING; OBSTACLE SCATTERING;

SCATTERING;

EID: 16244379216     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036139903435413     Document Type: Article

References (19)

1. D. COLTON AND R. KRESS, Integral Equation Methods in Scattering Theory, John Wiley and Sons, New York, 1983.
2. D. COLTON AND R. KRESS, Inverse Acoustic and Electromagnetic Scattering Theory, 2nd ed., Springer-Verlag, Berlin, Heidelberg, New York, 1998.
3. F. HETTLICH, Fréchet derivatives in inverse obstacle scattering, Inverse Problems, 11 (1995), pp. 371-382.
4. F. HETTLICH, Erratum: Fréchet derivatives in inverse obstacle scattering, Inverse Problems, 14 (1998), pp. 209-210.
5. F. HETTLICH, The Domain Derivative in Inverse Obstacle Scattering, Habilitation, Erlangen, 1999.
6. T. HOHAGE, Iterative Methods in Inverse Obstacle Scattering: Regularization Theory of Linear and Nonlinear Exponentially Ill-Posed Problems, dissertation, Linz University, Linz, Austria, 1999.
7. A. KIRSCH, The domain derivative and two applications in inverse scattering theory, Inverse Problems, 9 (1993), pp. 81-96.
8. R. KRESS, Electromagnetic waves scattering: Specific theoretical tools, in Scattering, E. R. Pike and P. C. Sabatier, eds., Academic Press, London, 2001, pp. 175-190.
9. R. KRESS, Electromagnetic waves scattering: Scattering by obstacles, in Scattering, E. R. Pike and P. C. Sabatier, eds., Academic Press, London, 2001, pp. 191-210.
10. R. KRESS, Uniqueness in inverse obstacle scattering, in New Analytic and Geometric Methods in Inverse Problems, K. Bingham, Y. V. Kurylev, and E. Somersalo, eds, Springer-Verlag, Berlin, Heidelberg, New York, 2004, pp. 323-336.
11. R. KRESS AND L. PÄIVÄRINTA, On the far field in obstacle scattering, SIAM J. Appl. Math., 59 (1999), pp. 1413-1426.
12. R. KRESS AND W. RUNDELL, Inverse scattering for shape and impedance, Inverse Problems, 17 (2001), pp. 1075-1085.
13. C.M. MORREY, Multiple Integrals in the Calculus of Variations, Springer-Verlag, Berlin, Heidelberg, New York, 1966.
14. J.C. NÉDÉLEC, Acoustic and Electromagnetic Equations, Springer-Verlag, Berlin, Heidelberg, New York, 2001.
15. R. POTTHAST, Fréchet differentiability of boundary integral operators in inverse acoustic scattering, Inverse Problems, 10 (1994), pp. 431-447.
16. R. POTTHAST, Fréchet differentiability of the solution to the acoustic Neumann scattering problem with respect to the domain, J. Inverse Ill-posed Probl., 4 (1996), pp. 67-84.
17. R. POTTHAST, Domain derivatives in electromagnetic scattering, Math. Methods Appl. Sci., 19 (1996), pp. 1157-1175.
18. A. ROGER, Newton Kantorovich algorithm applied to an electromagnetic inverse problem, IEEE Trans. Antennas and Propagation, AP-29 (1981), pp. 232-238.
19. C. SCHORMANN, Analytische und numerische Untersuchungen bei inversen Transmission-sproblemen zur zeitharmonischen Wellengleichung, dissertation, University of Göttingen, Göttingen, Germany, 2000.