Fakultät für Mathematik
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Fakultät für Mathematik
Startseite
Institute
Institut für Angewandte und Numerische Mathematik
Arbeitsgruppe 4: Inverse Probleme
Prof. i. R. Dr. Andreas Kirsch
Publikationen

Publikationen

==== Before 1990 ====

  1. Continuous Perturbations of Infinite Optimization Problems. Journal of Optimization Theory and Applications 32 (1980), 171-182. https://doi.org/10.1007/BF00934722
  2. The Determination of the Surface Impedance of an Obstacle from Measurements of the Far Field Pattern. (With D. Colton) SIAM J. Appl. Math. 41 (1981), 8-15. https://doi.org/10.1137/0141002
  3. Optimal Control of an Exterior Robin Problem. J. Math. Anal. Appl.82 (1981), 144-151. https://doi.org/10.1016/0022-247X(81)90229-8
  4. Stable Methods for Solving the Inverse Scattering Problem for a Cylinder. (With D. Colton) Proc. Roy. Soc. Edinburgh, 89 A (1981), 181-188. https://doi.org/10.1017/S0308210500020217
  5. On the Continuity of the Metric Projection Onto a Convex Set Subject to an Additional Constraint. (With H. Engl) Bullettino della Unione Matematica Italiana, Ser. VI, Vol. I-A, N.~1 (1982)
  6. A Weak Bang-Bang Principle for the Control of an Exterior Robin Problem. Appl. Analysis 13 (1982), 62-75. https://doi.org/10.1080/00036818208839376
  7. The Three Dimensional Inverse Scattering Problem for Acoustic Waves. (With T. Angell und D. Colton) J. Diff. Equa. 46 (1982), 46-58. https://doi.org/10.1016/0022-0396(82)90108-5
  8. A Method for the Numerical Solution of the One-dimensional Inverse Stefan Problem. (With R.\,Reemtsen) Num. Math. 45 (1984), 253-273. https://doi.org/10.1007/BF01389470
  9. Dense Sets and Far Field Pattern in Acoustic Wave Propagation. (With D. Colton) SIAM J. Math. Anal. 15 (1984), 996-1006. https://doi.org/10.1137/0515076
  10. The Robin Problem for the Helmholtz Equation as a Singular Perturbation Problem. Numer. Funct. Anal. and Optimiz. 8 (1985), 1-20. https://doi.org/10.1080/01630568508816201
  11. The Denseness of the Far Field Patterns for the Transmission Problem. IMA J. Appl. Math. 37 (1986), 213-225. https://doi.org/10.1093/IMAMAT/37.3.213
  12. Two Methods for Solving the Inverse Acoustic Scattering Problem. (With R. Kress, P. Monk und A. Zinn) Inverse Problems 4 (1988), 749-769. https://doi.org/10.1088/0266-5611/4/3/013
  13. The Backus-Gilbert Method. (With B. Schomburg und G. Berendt) Inverse Problems 4 (1988), 771-783. https://doi.org/10.1088/0266-5611/4/3/014
  14. Karp's Theorem in Acoustic Scattering Theory. (With D. Colton) Proc. of the Amer. Math. Soc. 103 (1988), 783-788. https://doi.org/10.1090/S0002-9939-1988-0947658-0
  15. The Optimization of Directivity and Signal-to-Noise Ratio of an Arbitrary Antenna Array. (With P. Wilde) Math. Meth. Appl. Sci. 10 (1988), 153-164. https://doi.org/10.1002/mma.1670100205
  16. Properties of Far Field Operators in Acoustic Scattering. Math. Meth. in the Appl. Sci. 11 (1989), 773-788. https://doi.org/10.1002/MMA.1670110604
  17. Surface Gradients and Continuity Properties for Some Integral Operators in Classical Scattering Theory. Math. Meth. in the Appl. Sci. 11 (1989), 789-804. https://doi.org/10.1002/MMA.1670110605
  18. Far Field Patterns for Acoustic Waves in an Inhomogeneous Medium. (With D. Colton und L. Paeivaerinta) SIAM J. Math. Anal. 20 (1989), 1472-1483. https://doi.org/10.1137/0520096

Between 1990 and 1999

  1. On the Necessary Conditions for Optimal Control of Retarded Systems. (Mit T. Angell) Appl. Math. Optim. 22 (1990), 117-145. https://doi.org/10.1007/BF01447323
  2. Convergence Analysis of a Coupled Finite Element and Spectral Method in Acoustic Scattering. (With P. Monk) IMA J. Num. Anal. 9 (1990), 425-447. https://doi.org/10.1093/imanum/10.3.425
  3. Antenna Control and Optimization. (With T.S. Angell and R.E. Kleinman) Proc. of the IEEE 79 (1991), 1559-1568. https://doi.org/10.1109/5.104230
  4. An Approximation Problem in Inverse Scattering Theory. (With D. Colton) Appl. Analysis 41 (1991), 23-32. https://doi.org/10.1080/00036819108840014
  5. The Use of Polarization Effects in Electromagnetic Inverse Scattering Problems. (With D.L. Colton) Math. Meth. in the Apl. Sci. 15 (1992), 1-10. https://doi.org/10.1002/MMA.1670150102
  6. Three-Dimensional Earth Conductivity Inversion. (With Z. Xiong) JCAM 42 (1992), 109-122. https://doi.org/10.1016/0377-0427(92)90166-U
  7. Multicriteria Optimization in Antenna Design. (With T.S. Angell) Math. Meth. in the Appl. Sci. 15 (1992), 647-660. https://doi.org/10.1002/MMA.1670150905
  8. The Conductive Boundary Condition for Maxwell's Equations. (With T.S. Angell) SIAM J. Appl. Math. 52 (1992), 1597-1610. https://doi.org/10.1137/0152092
  9. Remarks on Some Notions of Weak Solutions for the Helmholtz Equation. Appl. Anal. 47 (1992), 7-24. https://doi.org/10.1080/00036819208840128
  10. The Domain Derivative and Two Applications in Inverse Scattering Theory. Inverse Problems 9 (1993), 81-96. https://doi.org/10.1088/0266-5611/9/1/005
  11. Uniqueness in Inverse Scattering. (With R. Kreß) Inverse Problems 9 (1993), 285-299. https://doi.org/10.1088/0266-5611/9/2/009
  12. Diffraction by Periodic Structures. In: Inverse Problems in Mathematical Physics. (Eds.: L. Päivärinta und E. Somersalo), Lecture Notes in Physics 422, Springer, 1993. https://doi.org/10.1007/3-540-57195-7_11
  13. Target Signatures for Imperfectly Conducting Obstacles at Fixed Frequency. (With D.L. Colton) Q. J. Mech. appl. Math. 47 (1994), 1-15. https://doi.org/10.1093/qjmam/47.1.1
  14. Uniqueness Theorems in Inverse Scattering Theory for Periodic Structures. Inverse Problems 10 (1994), 145-152. https://doi.org/10.1088/0266-5611/10/1/011
  15. 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. https://doi.org/10.1093/imanum/14.4.523
  16. 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. https://doi.org/10.1137/S0036139993259891
  17. A Simple Method for Solving Inverse Scattering Problems in the Resonance Region. (With D. Colton) Inverse Problems 12 (1996), 383-393. https://doi.org/10.1088/0266-5611/12/4/003
  18. Schiffer's Theorem in Inverse Scattering Theory for Periodic Structures. (With F. Hettlich) Inverse Problems 13 (1997), 351-361. https://doi.org/10.1088/0266-5611/13/2/010
  19. A Bicriterial Optimization Problem of Antenna Design. (Mit A. Jüschke und J. Jahn) Comput. Optim. and Applic. 7 (1997), 261-276. https://doi.org/10.1023/A:1008611827855
  20. 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. https://doi.org/10.1137/S003613999732768X
  21. On Recovering Obstacles Inside Inhomogeneities. (With L. Päivärinta) Math. Meth. in the Appl. Sci. 21 (1998), 619-651. https://doi.org/10.1002/(SICI)1099-1476(19980510)21:7<619::AID-MMA940>3.0.CO;2-P
  22. Characterization of the Scattering Obstacle by the Spectral Data of the Far Field Operator. Inverse Problems 14 (1998), 1489-1512. https://doi.org/10.1088/0266-5611/14/6/009
  23. 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. https://doi.org/10.1002/(SICI)1099-1476(19990125)22:2<177::AID-MMA36>3.0.CO;2-F
  24. Factorization of the Far Field Operator for the Inhomogeneous Medium Case and an Application in Inverse Scattering Theory. Inverse Problems 15 (1999), 413-429. https://doi.org/10.1088/0266-5611/15/2/005

Between 2000 and 2009

  1. A Linear Sampling Method for Inverse Scattering from an Open Arc. (With S. Ritter) Inverse Problems 16 (2000), 89-105. https://doi.org/10.1088/0266-5611/16/1/308
  2. The Linear Sampling Method in Inverse Scattering Theory. (With D. Colton and 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. https://doi.org/10.1007/978-3-7091-6296-5_6
  3. New Characterizations of Solutions in Inverse Scattering Theory. Applicable Analysis 76 (2000), 319-350. https://doi.org/10.1080/00036810008840888
  4. 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. https://doi.org/10.1216/jiea/1020282209
  5. 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. https://doi.org/10.1515/jiip.2002.10.2.171
  6. The MUSIC-Algorithm and the Factorization Method in Inverse Scattering Theory for Inhomogeneous Media. Inverse Problems 18 (2002), 1025-1040. https://doi.org/10.1088/0266-5611/18/4/306
  7. A Finite Element Method for Approximating Electromagnetic Scattering from a Conducting Object (With P. Monk). Numerische Mathematik 92 (2002), 501-534. https://doi.org/10.1007/s002110100346
  8. The Factorization Method in Inverse Scattering from Periodic Structures. (with T. Arens) Inverse Problems 19 (2003), 1195-1211. https://doi.org/10.1088/0266-5611/19/5/311
  9. 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. https://doi.org/10.1016/j.matcom.2004.02.011
  10. Schlecht gestellte Probleme - Oder wenn das Ungenaue genauer ist. (With U. Kirchgraber and D. Stoffer) Mathematische Semesterberichte 51 (2004), 175-205. https://doi.org/10.1007/s00591-004-0086-1
  11. The Factorization Method for Maxwell's Equations. Inverse Problems 20 (2004), S117-S134. https://doi.org/10.1088/0266-5611/20/6/S08
  12. The Factorization Method for a Class of Inverse Elliptic Problems. Math. Nachrichten 278 (2005), 258-277. https://doi.org/10.1002/mana.200310239
  13. A Sampling Method for Detecting Buried Objects Using Electromagnetic Scattering. (With B. Gebauer, M. Hanke-Bourgeois, W. Muniz) Inverse Problems 21 (2005), 2035-2050. https://doi.org/10.1088/0266-5611/21/6/015
  14. The factorization method in inverse elastic scattering from penetrable bodies. (With A.Charalambopoulos, K.Anagnostopoulos, D. Gintides, K. Kiriaki) Inverse Problems 23 (2007) 27–51. https://doi.org/10.1088/0266-5611/23/1/002
  15. An Integral Equation Approach and the Interior Transmission Problem for Maxwell's Equations. Inverse Problems and Imaging 1 (2007), 107-127. https://doi.org/10.3934/ipi.2007.1.159
  16. 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. https://doi.org/10.1216/jiea/1190905490
  17. On the Existence of Transmission Eigenvalues. Inverse Problems and Imaging 3 (2009), 155-172. https://doi.org/10.3934/IPI.2009.3.155
  18. 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. https://doi.org/10.1080/00036810903042125

Since 2010

  1. On the Interior Transmission Eigenvalue Problem. (With F. Cakoni) Int. Jour. of Comp. Sci. Math. 3 (2010), 142-167. https://doi.org/10.1504/IJCSM.2010.033932
  2. A Factorization Scheme for Determining Conductivity Contrasts in Impedance Tomography. (With S. Schmitt) Inverse Problems 27 (2011). https://doi.org/10.1088/0266-5611/27/9/095005
  3. The Factorization Method for an Inverse Fluid-Solid Interaction Scattering Problem. (With A. Ruiz) Inverse Problems and Imaging 6 (4) (2012), 681-695. https://doi.org/10.3934/ipi.2012.6.681
  4. Simultaneous Reconstructions of Absorption Density and Wave Speed with Photoacoustic Measurements. (With O. Scherzer) SIAM J. Appl. Math.72 (5) (2012).. https://doi.org/10.1137/110849055
  5. The Factorization Method for a Conductive Boundary Condition. (With A. Kleefeld) J. Int. Equ. Appl.24 (2012), 575-601. https://doi.org/10.1216/JIE-2012-24-4-575
  6. Some Inverse Problems Arizing From Elastic Scattering by Rigid Bodies. (With G. Hu and M. Sini) Inverse Problems 29 (2013). https://doi.org/10.1088/0266-5611/29/1/015009
  7. Direct and Inverse Acoustic Scattering by a Mixed-Type Scatterer. (With X. Liu) Inverse Problems 29 (6), (2013). https://doi.org/10.1088/0266-5611/29/6/065005
  8. The Factorization Method for Inverse Acoustic Scattering in a Layered Medium. (With O. Bondarenko and X. Liu) Inverse Problems 29 (2013). https://doi.org/10.1088/0266-5611/29/4/045010
  9. The Inside-Outside Duality for Scattering Problems by Inhomogeneous Media. (With A. Lechleiter) Inverse Problems 29 (10) (2013). https://doi.org/10.1088/0266-5611/29/10/104011
  10. 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. https://doi.org/10.1002/mma.2877
  11. 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. https://doi.org/10.1002/mma.3037
  12. Seismic Tomography is Locally Illposed. (With A. Rieder) Inverse Problems 30 (2014). https://doi.org/10.1088/0266-5611/30/12/125001
  13. A Modification of the Factorization Method for the Classical Acoustic Inverse Scattering Problems. (With X. Liu) Inverse Problems 30 (3), (2014). https://doi.org/10.1088/0266-5611/30/3/035013
  14. 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. https://doi.org/10.1515/jiip-2014-0021
  15. A Note on Sylvester's Proof of Discreteness of Interior Transmission Eigenvalues. C. R. Acad. Sci. Paris, Ser. I (2016). https://doi.org/10.1016/j.crma.2016.01.015
  16. 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. https://doi.org/10.3934/ipi.2016.10.103
  17. Inverse Problems for Abstract Evolution Equations With Applications in Electrodynamics And Elasticity. (with A. Rieder) Inverse Problems 32 (8), 2016. https://doi.org/10.5445/IR/1000051550
  18. The Factorization Method for Inverse Scattering by a Penetrable Anisotropic Obstacle with Conductive Boundary Condition. (With O. Bondarenko) Inverse Problems 32 (10), (2016). https://doi.org/10.1088/0266-5611/32/10/105011
  19. Remarks on the Born Approximation and the Factorization Method. Applicable Analysis 96 (2017), 70-84. https://doi.org/10.1080/00036811.2016.1188286
  20. The definition and measurement of electromagnetic chirality. (With T. Arens, F. Hagemann, F. Hettlich) Math. Meth. Appl. Sci. 41 (2), (2017). 559-572. https://doi.org/10.1002/mma.4628
  21. The Limiting Absorption Principle and a Radiation Condition for the Scattering by a Periodic Layer. (With A. Lechleiter) SIAM J. Math. Anal. 50 (3) (2018), 2536-2565. https://doi.org/10.1137/17M1118920
  22. A Radiation Condition Arising from the Limiting Absorption Principle for a Closed Full‐ or Half‐Waveguide Problem. (With A. Lechleiter) Math. Meth. Appl. Sci. (2018). https://doi.org/10.1002/mma.4879
  23. Scattering by a Periodic Tube in R^3, Part i: A Limiting Absorption Principle. Inverse Problems 35 (10), (2019). https://dx.doi.org/10.1088/1361-6420/ab2e31
  24. Scattering by a Periodic Tube in R^3, Part ii: A Radiation Condition. Inverse Problems 35 (10), (2019). https://dx.doi.org/10.1088/1361-6420/ab2e27
  25. Inverse Problems for Abstract Evolution Equations II: Higher Order Differentiability for Viscoelasticity. (With A. Rieder) SIAM J. APPL. MATH. 79 (6), (2019), 2639-2662. https://doi.org/10.1137/19M1269403