Recent publications (since 2000)

Books

  1. Linear Integral Equations, third edition. Springer, New York, 2014.
  2. Integral Equation Methods in Scattering Theory. Classics in Applied Mathematics Vol. 72, SIAM, Philadelphia,  2013 (with D. Colton).
  3. Inverse Acoustic and Electromagnetic Scattering Theory, third edition. Springer, New York, 2013 (with D. Colton).
  4. Inverse Acoustic and Electromagnetic Scattering Theory, fourth edition. Springer, New York, 2019 (with D. Colton).
Papers

  1. The vector Helmholz equation revisited: Inverse obstacle scattering. J. Math. Anal. Appl. 519, 126821 (2023).
  2. The DB boundary condition in electromagnetic scattering revisited. SIAM J. Math. Anal. 53, 3661–3680 (2021).
  3. Some old and some new results in inverse obstacle scattering. In: Maxwell’s Equations (Langer et al, eds), Radon Series on Computational and Applied Mathematics, de Gruyter, Berlin, 259-283 (2019).
  4. Nonlocal impedance conditions in direct and inverse obstacle scattering. Inverse Problems 35, 024002 (2019).
  5. Hugo Steinhaus. Laudatio anlässlich der Enthüllung einer Gedenktafel. In: Göttinger Jahrbuch, Verlag Die Werkstatt, Göttingen, 223-230 (2019).
  6. Looking back on inverse scattering theory. SIAM Review 60, 779-807 (2018) (with D. Colton).
  7. Inverse scattering for shape and impedance revisited.  Jour. Integral Equations and Appl., 30, 293-311 (2018) (with W. Rundell).
  8. Integral equation methods in inverse obstacle scattering with a generalized impedance boundary condition.  In: Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan (J. Dick, F. Y. Kuo, H. Wozniakowski, eds.), Springer,  New York, 721-740 (2018).
  9. A boundary integral equation for the transmission eigenvalue problem for Maxwell's equation. Math. Meth. Appl. Science 41, 1316-1330 (2018) (with F. Cakoni, O. Ivanyshyn and F. Le Louer).
  10. Nonlinear integral equations for Bernoulli's free boundary value problem in three dimensions.  Comput. Math.  Appl. 74, 2784-2791 (2017) (with O. Ivanyshyn).
  11. On Trefftz' integral equation for the Bernoulli free boundary value problem.  Numerische Mathematik 136,  503-522 (2017).
  12. A boundary integral equation method for the transmission eigenvalue problem. Applicable Analysis 96, 23-38 (2017) (with F. Cakoni).
  13. A conformal mapping algorithm for the Bernoulli free boundary value problem. Math. Meth. Appl. Science 39, 2477-2487 (2016) (with H. Haddar).
  14. A nonlinear integral equation and an iterative algorithm for an inverse source problem. Jour. Integral Equations and Appl. 26, 179-198 (2015) (with W. Rundell).
  15. Integral equations. In: The Princeton Companion to Applied Mathematics (Higham et al, eds.) Princeton University Press, Princeton, 200-207 (2015).
  16. Simultaneous reconstruction of shape and generalized impedance functions in electrostatic imaging. Inverse Problems 30, 105009 (2014) (with F. Cakoni and Yuging Hu).
  17. A collocation method for a hypersingular boundary integral equation via trigonometric differentiation. Jour. Integral Equations and Appl. 26, 197-213 (2014).
  18. A conformal mapping method in inverse obstacle scattering. Complex Variables and Elliptic Equations 59, 863-882  (2014) (with H. Haddar).
  19. Reconstruction of extended sources for the Helmholtz equation. Inverse Problems 29, 035005 (2013) (with W. Rundell).
  20. Integral equation methods for the inverse obstacle problem with generalized impedance boundary condition. Inverse Problems 29, 015005 (2013)  (with F. Cakoni).
  21. An iterative method for a two-dimensional inverse scattering problem for a dielectric. Jour. on Inverse and Ill-Posed Problem 20, 575-590 (2012) (with A. Altundag).
  22. Inverse problems and conformal mapping. Complex Variables and Elliptic Equations 57, 301-316 (2012).
  23. On a two-dimensional inverse scattering problem for a dielectric. Applicable Analysis 91, 757-771 (2012) (with A. Altundag).
  24. A second degree Newton method for an inverse obstacle scattering problem. J. Comp. Phys. 230, 7661-7669 (2011) (with Kuo-Ming Lee).
  25. Electrical impedance tomography using a point electrode inverse scheme for complete electrode data. Inverse Problems and Imaging 5, 355-369 (2011) (with F. Delbary).
  26. Conformal mapping and impedance tomography. In: International Conference on Inverse Problems 2010, Hong Kong, (Hon and Ling, eds). J. Physics: Conference Series 290, 012009 (2011).
  27. Inverse scattering for surface impedance from phase-less far field data. J. Comp. Phys. 230, 3443-3452 (2011) (with O. Ivanyshyn).
  28. Inverse scattering. In: Handbook of Mathematical Methods in Imaging (Scherzer, ed.)  Springer, Berlin New York, 551-598 (2011) (with D. Colton).
  29. Simultaneous reconstruction of shape and impedance in corrosion detection. Methods and Applications of Analysis, 17, 357-378 (2010) (with F. Cakoni and C. Schuft).
  30. Integral equations for shape and impedance reconstruction in corrosion detection. Inverse Problems, 26, 095012 (2010) (with F. Cakoni and C. Schuft).
  31. Electrical impedance tomography with point sources. Jour. Integral Equations and Appl. 22, 193-216 (2010) (with F. Delbary).
  32. Conformal mapping and impedance tomography. Inverse Problems 26, 074002 (2010) (with H. Haddar).
  33. Identification of sound-soft 3D obstacles from phaseless data. Inverse Problems and Imaging 4, 131-149 (2010) (with O. Ivanyshyn).
  34. Huygens' principle and iterative methods in inverse obstacle scattering. Advances in Computational Mathematics 33, 413-429 (2010) (with O. Ivanyshyn and P. Serranho).
  35. Thirty years and still counting. Inverse Problems and Imaging 3, 151-153 (2009) (with D. Colton).
  36. Inverse scattering for an impedance cylinder. Inverse Problems in Science and Engineering 17, 473-488 (2009) (with F. Yaman, A. Yapar and I. Akduman). 
  37. A second order Newton method for sound soft inverse obstacle scattering.   Jour. on Inverse and Ill-Posed Problems 17, 173-185 (2009) (with N. Tezel and F. Yaman).
  38. Iterative and range test method for an inverse source problem for acoustic waves.  Inverse Problems 25, 055005 (2009) (with C. Alves and P. Serranho).
  39. Mathematische Methoden in Medizin und Technik: Inverse Probleme und Tomographie.  In: Zahlen, Formeln, ungelöste Rätsel. Georgia Augusta. Wissenschaftsmagazin der Georg-August-Universität Göttingen. Ausgabe 6, 88-95 (2008).
  40. Iterative methods for planar crack reconstruction in semi-infinite domains. Jour. on Inverse and Ill-Posed Problems 16, 743-761 (2008) (with N. Vintonyak).
  41. Nonlinear integral equations for the complete electrode model in inverse impedance tomography. Applicable Analysis 87, 1267-1288 (2008) (with H. Eckel).
  42. Inverse electromagnetic scattering in a two-layered medium with an application to mine detection. Inverse Problems 24,  015002 (2008) (with F. Delbary, K. Erhard, R. Potthast and J. Schulz).
  43. Inverse scattering for planar cracks via nonlinear integral equations. Math. Meth. Appl. Sciences 31, 1221-1232 (2008) (with O. Ivanyshyn).
  44. Integral equations for an inverse boundary value problem for the two-dimensional Stokes equations. Jour. on Inverse and Ill-Posed Problems 15, 461-481 (2007) (with C. Alves and A. Silvestre).
  45. Uniqueness and numerical methods in inverse obstacle scattering. In: Inverse Problems in Applied Sciences--towards breakthrough (Cheng et al, eds). J. Physics: Conference Series 73, 012003 (2007).
  46. Integral equations for inverse problems in corrosion detection from partial Cauchy data. Inverse Problems and Imaging 1, 229-245 (2007) (with F. Cakoni).
  47. Nonlinear integral equations for the inverse electrical impedance problem. Inverse Problems 23, 475-491 (2007) (with H. Eckel) .
  48. A hybrid method for sound-hard obstacle reconstruction. J. Comput. Appl. Math. 24, 418-427 (2007) (with P. Serranho).
  49. Conformal mapping and an inverse impedance boundary value problem.  Jour. on Inverse and Ill-Posed Problems 14, 785-804 (2006) (with H. Haddar).
  50. Nonlinear integral equations in inverse obstacle scattering. In: Mathematical Methods in Scattering Theory and Biomedical Engineering (Fotiatis, Massalas, eds).  World Scientific, Singapore,  39-50 (2006)  (with O. Ivanyshyn).
  51. Nonlinear integral equations for solving inverse boundary value problems for inclusions and cracks.  Jour. Integral Equations and Appl. 18, 13-38 (2006) (with O. Ivanyshyn). Corrigendum
  52. Iterative reconstruction of dielectric rough surface profiles at fixed frequency.  Inverse Problems 22, 939-954 (2006) (with I. Akduman and A. Yapar).
  53. Using fundamental solutions in inverse scattering. Inverse Problems 22, R49-R66 (2006) (with D. Colton).
  54. One-dimensional profile inversion in a cylindrical layer with inhomogeneous impedance boundary: A Newton-type iterative solution.   IEEE Transaction on Geoscience and Remote Sensing, 43, 2192-2199 (2005) (with A. Yapar,  H. Sahintürk and I. Akduman).
  55. Nonlinear integral equations and the iterative solution for  an inverse boundary value problem. Inverse Problems 21, 1207-1223 (2005)  (with W. Rundell).
  56. Conformal mappings and inverse boundary value problems. Inverse Problems 21, 935-953 (2005) (with H. Haddar). 
  57. A hybrid method for two-dimensional  crack reconstruction. Inverse Problems  21, 773-784 (2005) (with P.Serranho). 
  58. A hybrid method for inverse boundary value problems in potential theory. Jour. on Inverse and Ill-Posed Problems 13, 27-40 (2005) (with R. Chapko).
  59. On the Frechet derivative for obstacle scattering with an impedance boundary condition. SIAM J. Appl. Math. 65, 194-208 (2004) (with H. Haddar). 
  60. Decomposition methods in inverse obstacle scattering via Newton iteration. In: Advances in Scattering and Biomedical Engineering (Fotiatis, Massalas, eds).  World Scientific, Singapore,  91-102 (2004).
  61. Inverse Dirichlet problem and conformal mapping.  Mathematics and Computers in Simulation  66, 255-265 (2004). 
  62. Uniqueness in inverse obstacle scattering.  In: New Analytic and Geometric Methods in Inverse Problems (Bingham, Kurylev, Somersalo, eds). Springer-Verlag, Berlin Heidelberg New York,  323-336 (2004). 
  63. Newton's method for inverse obstacle scattering meets the method of least squares. Inverse Problems 19, S91-S104 (2003). 
  64. Integral equation methods for scattering from an impedance crack.  J. Comput. Appl. Math.  161, 161-177 (2003)  (with Kuo-Ming Lee). 
  65. A factorisation method for an inverse Neumann problem for harmonic vector fields.  Georgian Math. Journal 10, 549-560 (2003). 
  66. Direct and inverse scattering problems for inhomogeneous impedance cylinders of arbitrary shape.  Radio Science 38,  1055-1064 (2003) (with I. Akduman). 
  67. Uniqueness in inverse obstacle scattering for electromagnetic waves. Proceedings of the URSI General Assembly 2002, Maastricht. 
  68. Electrostatic imaging via conformal mapping.  Inverse Problems 18, 1659-1672 (2002) (with I. Akduman). 
  69. A sampling method for an inverse boundary value problem for harmonic vector fields. In: Ill-Posed and Inverse Problems (Kabanikhin, Romanov, eds) pp. 243-262, VSP,  Utrecht, 2002 . 
  70. Linear sampling methods for inverse boundary value problems in potential theory.  Appl. Numer. Math. 43, 161-173 (2002) (with L. Kühn). 
  71. Reconstruction of a current distribution from its magnetic field. Inverse Problems 18, 1127-1146  (2002) (with L. Kühn and R. Potthast). 
  72. Acoustic scattering: Specific theoretical tools. In: Scattering (Pike, Sabatier, eds.) pp. 37-51, Academic Press, London, 2001. 
  73. Acoustic scattering: Scattering by obstacles. In: Scattering (Pike, Sabatier, eds.) pp. 52-73, Academic Press, London, 2001. 
  74. Electromagnetic waves scattering: Specific theoretical tools. In: Scattering (Pike, Sabatier, eds.) pp. 175-190, Academic Press, London, 2001. 
  75. Electromagnetic waves scattering: Scattering by obstacles. In: Scattering (Pike, Sabatier, eds.) pp. 191-210, Academic Press, London, 2001.
  76. On the denseness of Herglotz wave functions and electromagnetic Herglotz pairs in Sobolev spaces. Math. Meth. in the Appl. Sci. 24, 1289-1303 (2001) (with D. Colton).
  77. Inverse scattering for shape and impedance. Inverse Problems 17, 1075-1085 (2001) (with W. Rundell).
  78. Iterative solution of the inverse scattering problem for a locally perturbed half-plane. In: Kleinheubacher Berichte 44, pp. 400-411, T-Nova Deutsche Telekom Innovationsgesellschaft (2001). 
  79. Numerical methods in inverse obstacle scattering. ANZIAM J. 42 (E), C44-C67 (2000). 
  80. Inverse obstacle scattering with modified or reduced data. In: Scattering Theory and Biomedical Engineering Modelling and Applications (Dassios et. al., eds). World Scientific, Singapore, 10-18 (2000). 
  81. Uniqueness for a linearized inverse obstacle problem using backscattering data. In: Proceedings of the Fifth International Conference on Mathematical and Numerical Aspects of Wave Propagation (Bermudez et al, eds). pp. 489-493 SIAM Publications, Philadelphia, 2000 (with P. Hähner).
  82. On the numerical solution of a hypersingular integral equation for elastic scattering from a planar crack. IMA J. Numer. Anal. 20, 601-619 (2000) (with R. Chapko and L. Mönch).
  83. Inverse scattering for a locally perturbed half-plane. Inverse Problems 16, 1541-1559 (2000) (with T. Tran). 
  84. Integral equation methods in inverse obstacle scattering. ANZIAM J. 42, 65-78 (2000). 
  85. Obstacle scattering as seen by R.K. and R.K. In: Analytical and Computational Methods in Scattering and Applied Mathematics (Santosa, Stakgold, eds). Clapman & Hall/CRC, Boca Raton, 165-175 (2000). 
  86. Inverse obstacle scattering with modified or reduced data. Z. angew. Math. Mech. 80, Suppl. 1, S229-S232 (2000). 
  87. On the numerical solution of initial boundary value problems by the Laguerre transformation and boundary integral equations. In: Integral and Integrodifferential Equations: Theory, Methods and Applications Series in Mathematical Analysis and Applications, Vol. 2 (Agarwal, O'Regan, eds). Gordon and Breach Science Publishers, Amsterdam, 55-69 (2000) (with R. Chapko). 
  88. An inverse boundary value problem for the Oseen equation. Math. Meth. in the Appl. Sci. 23, 103-120 (2000) (with S. Meyer).