Department of Mathematics
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Department of Mathematics
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Institutes
Institute for Applied and Numerical Mathematics
Research Group 4: Inverse Problems
Prof. Dr. Andreas Kirsch
Publications

Publications

  1. Convergence Analysis of a Coupled Finite Element and Expansion Method in Acoustic Scattering. (With P. Monk) IMA J. Num. Anal. 9 (1990), 425-447.
  2. Antenna Control and Optimization. (With T.S. Angell and R.E. Kleinman) Proc. of the IEEE 79 (1991), 1559-1568.
  3. An Approximation Problem in Inverse Scattering Theory. (With D. Colton) Appl. Analysis 41 (1991), 23-32.
  4. The Use of Polarization Effects in Electromagnetic Inverse Scattering Problems. (With D.L. Colton) Math. Meth. in the Apl. Sci. 15 (1992), 1-10.
  5. Three-Dimensional Earth Conductivity Inversion. (With Z. Xiong) JCAM 42 (1992), 109-122.
  6. Multicriteria Optimization in Antenna Design. (With T.S. Angell) Math. Meth. in the Appl. Sci. 15 (1992), 647-660.
  7. The Conductive Boundary Condition for Maxwell's Equations. (With T.S. Angell) SIAM J. Appl. Math. 52 (1992), 1597-1610.
  8. Remarks on Some Notions of Weak Solutions for the Helmholtz Equation. Appl. Anal. 47 (1992), 7-24.
  9. The Domain Derivative and Two Applications in Inverse Scattering Theory. Inverse Problems 9 (1993), 81-96.
  10. Uniqueness in Inverse Scattering. (With R. Kreß) Inverse Problems 9 (1993), 285-299.
  11. Diffraction by Periodic Structures. In: Inverse Problems in Mathematical Physics. (Eds.: L. Päivärinta und E. Somersalo), Lecture Notes in Physics 422, Springer, 1993.
  12. Target Signatures for Imperfectly Conducting Obstacles at Fixed Frequency. (With D.L. Colton) Q. J. Mech. appl. Math. 47 (1994), 1-15.
  13. Uniqueness Theorems in Inverse Scattering Theory for Periodic Structures. Inverse Problems 10 (1994), 145-152.
  14. An Analysis of the Coupling of Finite Element and Nyström Methods in Acoustic Scattering. (With P. Monk) IMA J. Num. Anal. 14 (1994), 523-544.
  15. A Finite Element/Spectral Method for Approximating the Time Harmonic Maxwell System in R^n. (With P. Monk) SIAM J. Appl. Math. 55 (1995), 1324-1344.
  16. p1-simple.pdf|A Simple Method for Solving Inverse Scattering Problems in the Resonance Region.(With D. Colton) Inverse Problems 12 (1996), 383-393.
  17. p2-hettlich.pdf|Schiffer's Theorem in Inverse Scattering Theory for Periodic Structures. (With F. Hettlich) Inverse Problems 13 (1997), 351-361.
  18. A Bicriterial Optimization Problem of Antenna Design. (Mit A. Jüschke und J. Jahn) Comput. Optim. and Applic. 7 (1997), 261-276.
  19. Corrigendum to: ``A Finite Element/Spectral Method for Approximating the Time Harmonic Maxwell System in R^n. SIAM J. Appl. Math. 55 (1995), 1324-1344.'' (with P. Monk) SIAM J. Appl. Math. 58 (1998), 2024-2028.
  20. p3-lassi.pdf|On Recovering Obstacles Inside Inhomogeneities. (With L. Päivärinta) Math. Meth. in the Appl. Sci. 21 (1998), 619-651.
  21. p4-charact.pdf|Characterization of the Scattering Obstacle by the Spectral Data of the Far Field Operator. Inverse Problems 14 (1998), 1489-1512.
  22. p5-ritter-nystr.pdf|The Nyström Method for Solving a Class of Singular Integral Equations and Applications in 3D-Plate Elasticity. (With S. Ritter) Math. Meth. in the Appl. Sci. 22 (1999), 177-197.
  23. p6-inhomo.pdf|Factorization of the Far Field Operator for the Inhomogeneous Medium Case and an Application in Inverse Scattering Theory. Inverse Problems 15 (1999), 413-429.
  24. p7-ritter-fac.pdf|A Linear Sampling Method for Inverse Scattering from an Open Arc. (With S. Ritter) Inverse Problems 16 (2000), 89-105.
  25. The Linear Sampling Method in Inverse Scattering Theory. (Mit D. Colton und P. Monk) In: Surveys on Solution Methods for Inverse Problems (Eds.: D. Colton, H.W. Engl, A. Louis, J.R. McLaughlin, W. Rundell), Springer Vienna/New York, 2000.
  26. p8-new-char.pdf|New Characterizations of Solutions in Inverse Scattering Theory. Applicable Analysis 76 (2000), 319-350.
  27. p9-ChanWil-nystr.pdf|A Nyström Method for a Class of Integral Equations on the Real Line with Applications to Scattering by Diffraction Gratings and Rough Surfaces. (with A. Meier, T. Arens, S.N. Chandler-Wilde). J. Integral Equations And Applications 12 (2000), 281-321.
  28. p10-imp-grinberg.pdf|The Linear Sampling Method in Inverse Obstacle Scattering for Impedance Boundary Conditions. (with N. Grinberg) Journal of Inverse and Ill-Posed Problems 10 (2002), 171-185.
  29. p12-music.pdf|The MUSIC-Algorithm and the Factorization Method in Inverse Scattering Theory for Inhomogeneous Media. Inverse Problems 18 (2002), 1025-1040.
  30. p11-FE-monk.pdf|A Finite Element Method for Approximating Electro-Magnetic Scattering from a Conducting Object (With P. Monk). Numerische Mathematik 92 (2002), 501-534.
  31. p14-arens.pdf|The Factorization Method in Inverse Scattering from Periodic Structures. (with T.\,Arens) Inverse Problems 19 (2003), 1195-1211.
  32. p15-mix-grinberg.pdf|The Factorization Method for Obstacles with A-priori Separated Sound-Soft and Sound-Hard Parts. (With N.\,Grinberg) Mathematics and Computers in Simulation 66 (2004), 267-279.
  33. p13-factor.pdf|The Factorization Method for a Class of Inverse Elliptic Problems. Math. Nachrichten 278 (2005), 1-20.
  34. Schlecht gestellte Probleme - Oder wenn das Ungenaue genauer ist. (With U. Kirchgraber and D. Stoffer) Mathematische Semesterberichte 51 (2004), 175-205.
  35. p16-maxwell.pdf|The Factorization Method for Maxwell's Equations. Inverse Problems 20 (2004), S117-S134.
  36. p17-elliptic.pdf|The Factorization Method for a Class of Inverse Elliptic Problems. Math. Nachrichten 278 (2005), 258-277.
  37. p18-BMBF.pdf|A Sampling Method for Detecting Buried Objects Using Electromagnetic Scattering. (With B. Gebauer, M. Hanke-Bourgeois, W. Muniz) Inverse Problems 21 (2005), 2035-2050.
  38. p19-ITrP.pdf|An Integral Equation Approach and the Interior Transmission Problem for Maxwell's Equations. Inverse Problems and Imaging 1 (2006), 159-179.
  39. p20-Layer.pdf|An Integral Equation for Maxwell's Equations in a Layered Medium with an Application to the Factorization Method. J. Integral Equations and Applications 19 (2007), 333-358.
  40. p21-intEVP.pdf|On the Existence of Transmission Eigenvalues. Inverse Problems and Imaging 3 (2009), 155-172.
  41. p22-IeL2.pdf|The Operator Equations of Lippmann-Schwinger Type for Acoustic and Electromagnetic Scattering Problems in $L^2$. (With A. Lechleiter) Applicable Analysis 88 (6) (2009), 807-830.
  42. p23-ITREVP.pdf|On the Interior Transmission Eigenvalue Problem. (With F. Cakoni) Int. Jour. of Comp. Sci. Math. 3 (2010), 142-167.
  43. p24-ImpTom.pdf|A Factorization Scheme for Determining Conductivity Contrasts in Impedance Tomography. (With S. Schmitt) Inverse Problems 27 (2011), 095005.
  44. p25-Fluid.pdf|The Factorization Method for an Inverse Fluid-Solid Interaction Scattering Problem. (With A. Ruiz) Inverse Problems and Imaging 6 (4) (2012), 681-695.
  45. p26-Sini-Hu.pdf|Some Inverse Problems Arizing From Elastic Scattering by Rigid Bodies. (With G. Hu and M. Sini) Inverse Problems 29 (2013), 015009.
  46. p27-Scherzer.pdf|Simultaneous Reconstructions of Absorption Density and Wave Speed with Photoacoustic Measurements. (With O. Scherzer) SIAM J. Appl. Math.72 (5) (2012), 104005.
  47. p28-Kleefeld.pdf|The Factorization Method for a Conductive Boundary Condition. (With A. Kleefeld) J. Int. Equ. Appl.24 (2012), 575-601.
  48. p29-Liu.pdf|Direct and Inverse Acoustic Scattering by a Mixed-Type Scatterer. (With X. Liu) Inverse Problems 29 (6), (2013), 065005.
  49. p30-Bond-Liu.pdf|The Factorization Method for Inverse Obstacle Scattering with Conductive Boundary Condition. (With O. Bondarenko and X. Liu) Inverse Problems 29 (9) (2013), 095021.
  50. p31-Lechleiter.pdf|The Inside-Outside Duality for Scattering Problems by Inhomogeneous Media. (With A. Lechleiter) Inverse Problems 29 (10) (2013), 104011.
  51. p33-FM-Liu.pdf|The Factorization Method for Inverse Acoustic Scattering by a Penetrable Anisotropic Obstacle. (With X. Liu) Mathematical Methods in the Applied Sciences 37 (8) (2014), 1159-1170.
  52. p32-Rieder.pdf|On the Linearization of Operators Related to the Full Waveform Inversion in Seismology. (With A. Rieder) Math. Meth. Appl. Sci. 37 (18) (2014), 2995-3007
  53. p34-Rieder.pdf|Seismic Tomography is Locally Illposed. (With A. Rieder) Inverse Problems 30 (2014), 125001
  54. p40-Liu.pdf|A Modification of the Factorization Method for the Classical Acoustic Inverse Scattering Problems. (With X. Liu) Inverse Problems 30 (3), (2014) 035013
  55. p36-Hayk.pdf|The Interior Transmission Eigenvalue Problem for a Spherically-Symmetric Domain with Anisotropic Medium and a Cavity. (With H. Asatryan) Journal Inverse and Ill-Posed Problems 23 (4), (2014) 299–307.
  56. p37-sylv.pdf|A Note on Sylvester's Proof of Discreteness of Interior Transmission Eigenvalues. C. R. Acad. Sci. Paris, Ser. I (2016), http://dx.doi.org/10.1016/j.crma.2016.01.015
  57. p38-HuYin.pdf|Factorization Method in Inverse Interaction Problems with Bi-Periodic Interfaces Between Acoustic and Elastic Waves. (With G. Hu and T. Yin) Inverse Problems and Imaging 30 (1), (2016) 103-129.
  58. p42-Rieder.pdf|Inverse Problems for Abstract Evolution Equations With Applications in Electrodynamics And Elasticity. (with A. Rieder) Inverse Problems 32 (8), 2016
  59. p41-Bond.pdf|The Factorization Method for Inverse Scattering by a Penetrable Anisotropic Obstacle with Conductive Boundary Condition. (With O. Bondarenko) Inverse Problems 32 (10), (2016) 105011.
  60. p39-Born.pdf|Remarks on the Born Approximation and the Factorization Method. Applicable Analysis 96 (2017), 70-84.
  61. p43-Waveguide1.pdf|The Limiting Absorption Principle and a Radiation Condition for the Scattering by a Periodic Layer. (With A. Lechleiter) Submitted to: SIAM J. Math. Anal.