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Applicable Analysis
An International Journal
Volume 91, 2012 - Issue 4: Special Issue on Inverse Problems and Applications
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Original Articles

On a two-dimensional inverse scattering problem for a dielectric

Ahmet Altundag Institut für Numerische und Angewandte Mathematik, Universität Göttingen, 37083 Göttingen, Germany
&
Rainer Kress Institut für Numerische und Angewandte Mathematik, Universität Göttingen, 37083 Göttingen, GermanyCorrespondence[email protected]
Pages 757-771 | Received 29 Mar 2011, Accepted 30 Aug 2011, Published online: 27 Sep 2011

References

  • Colton , D and Kress , R . 1998 . Inverse Acoustic and Electromagnetic Scattering Theory, , 2nd. , Berlin : Springer .
  • Kirsch , A and Kress , R . 1993 . Uniqueness in inverse obstacle scattering . Inverse Prob. , 9 : 285 – 299 .
  • Johansson , T and Sleeman , B . 2007 . Reconstruction of an acoustically sound-soft obstacle from one incident field and the far-field pattern . IMA J. Appl. Math. , 72 : 96 – 112 .
  • Ivanyshyn , O and Kress , R . 2006 . “ Nonlinear integral equations in inverse obstacle scattering ” . In Mathematical Methods in Scattering Theory and Biomedical Engineering , Edited by: Fotiatis , DI and Massalas , CV . 39 – 50 . Singapore : World Scientific .
  • Ivanyshyn , O , Kress , R and Serranho , P . 2010 . Huygens' principle and iterative methods in inverse obstacle scattering . Adv. Comput. Math. , 33 : 413 – 429 .
  • Kress , R and Rundell , W . 2005 . Nonlinear integral equations and the iterative solution for an inverse boundary value problem . Inverse Probl. , 21 : 1207 – 1223 .
  • Eckel , H and Kress , R . 2007 . Nonlinear integral equations for the inverse electrical impedance problem . Inverse Probl. , 23 : 475 – 491 .
  • Hohage , T and Schormann , C . 1998 . A Newton-type method for a transmission problem in inverse scattering . Inverse Probl. , 14 : 1207 – 1227 .
  • Zinn , A . 1991 . “ The numerical solution of an inverse scattering problem for time-harmonic acoustic waves ” . In Inverse Problems and Imaging, Pitman Research Notes in Mathematics Series , Edited by: Roach , GF . Vol. 245 , 242 – 263 . London : Longman .
  • Colton , D and Kress , R . 1983 . Integral Equation Methods in Scattering Theory , New York : Wiley-Interscience Publications .
  • Kress , R and Roach , GF . 1978 . Transmission problems for the Helmholtz equation . J. Math. Phys. , 19 : 1433 – 1437 .
  • Kress , R . 1998 . Integral Equations, , 2nd , Berlin : Springer Verlag .
  • McLean , W . 2000 . Strongly Elliptic Systems and Boundary Integral Equations , Cambridge , , UK : Cambridge University Press .
  • Kress , R and Sloan , IH . 1993 . On the numerical solution of a logarithmic integral equation of the first kind for the Helmholtz equation . Numer. Math. , 66 : 199 – 214 .
  • Cakoni , F , Gintides , D and Haddar , H . 2010 . The existence of an infinite discrete set of transmission eigenvalues . SIAM J. Math. Anal. , 42 : 237 – 255 .
  • Ivanyshyn , O and Johansson , T . 2007 . Boundary integral equations for acoustical inverse sound-soft scattering . J. Inverse Ill-Posed Probl. , 15 : 1 – 14 .
  • Kress , R . 1995 . On the numerical solution of a hypersingular integral equation in scattering theory . J. Comput. Appl. Math. , 61 : 345 – 360 .

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