Publications of Prof. Dr. Armin Lechleiter

Book Chapters (2)

1. A. Lechleiter.
   Factorization method in inverse scattering.
   Encyclopedia of Applied and Computational Mathematics, B. Engquist (Eds.), pp. 479-485, Springer Verlag, 2016.

   online at: Link

2. A. Lechleiter.
   An introduction to direct and inverse scattering theory.
   Photonic Crystals: Mathematical Analysis and Numerical Approximation, Oberwolfach Seminars Vol.42, pp. 79-126, Birkhäuser, 2011.

   DOI: 10.1007/978-3-0348-0113-3
   online at: Link

Articles (58)

1. F. Bürgel, K. Kazimierski, A. Lechleiter.
   IPscatt—A MATLAB Toolbox for the Inverse Medium Problem in Scattering.
   ACM Transactions on Mathematical Software, 45(4), 45:1–45:20, 2019.

   DOI: 10.1145/3328525

2. F. Cakoni, H. Haddar, A. Lechleiter.
   On the factorization method for a far field inverse scattering problem in the time domain.
   SIAM Journal on Mathematical Analysis, 51(2):854-872, 2019.

   DOI: 10.1137/18M1214809

3. A. Konschin, A. Lechleiter.
   Reconstruction of a Local Perturbation in Inhomogeneous Periodic Layers from Partial Near Field Measurements.
   Inverse Problems, 35(11), 114006, IOPscience, 2019.

   DOI: 10.1088/1361-6420/ab1c66
   online at: https://iopscience.iop.org/article/10.1088/1361-6420/ab1c66

4. A. Kirsch, A. Lechleiter.
   A radiation condition arising from the limiting absorption principle for a closed full- or half-waveguide problem.
   Mathematical Methods in the Applied Sciences, 41(10):3955-3975, 2018.

   DOI: 10.1002/mma.4879

5. A. Lechleiter, R. Zhang.
   Reconstruction of Local Perturbations in Periodic Surfaces.
   Inverse Problems, 035006 34(2018), IOPscience, 2018.

   DOI: doi.org/10.1088/1361-6420/aaa7b1

6. A. Kirsch, A. Lechleiter.
   The limiting absorption principle and a radiation condition for the scattering by a periodic layer.
   SIAM Journal on Mathematical Analysis, 50(3):2536-2565, 2018.

   DOI: 10.1137/17M1118920

7. A. Lechleiter, R. Zhang.
   A Convergent Numerical Scheme for Scattering of Aperiodic Waves from Periodic Surfaces Based on the Floquet-Bloch Transform.
   SIAM Journal on Numerical Analysis, 55(2):713-736, 2017.

   DOI: 10.1137/16M1067524

8. A. Lechleiter, R. Zhang.
   A Floquet-Bloch transform based numerical method for scattering from locally perturbed periodic surfaces.
   SIAM Journal on Scientific Computing, 39(5):B819-B839, 2017.

   DOI: 10.1137/16M1104111
   online at: http://epubs.siam.org/doi/pdf/10.1137/16M1104111

9. F. Bürgel, K. Kazimierski, A. Lechleiter.
   A sparsity regularization and total variation based computational framework for the inverse medium problem in scattering.
   Journal of Computational Physics, 339, 1–30, 2017.

   DOI: 10.1016/j.jcp.2017.03.011

10. A. Lechleiter, T. Rienmüller.
    Collocation discretization for an integral equation in ocean acoustics with depth-dependent speed of sound.
    Mathematical Methods in the Applied Sciences, 40(5):1608-1624, Wiley, 2017.

    DOI: 10.1002/mma.4082

11. A. Lechleiter, M. Rennoch.
    Non-linear Tikhonov Regularization in Banach Spaces for Inverse Scattering from Anisotropic Penetrable Media.
    Inverse Problems and Imaging, 11(1):151-176, 2017.

    DOI: 10.3934/ipi.2017008

12. A. Lechleiter, R. Zhang.
    Non-periodic acoustic and electromagnetic, scattering from periodic structures in 3D.
    Computers & Mathematics with Applications, 74(11): 2723-2738, 2017.

    online at: https://doi.org/10.1016/j.camwa.2017.08.042

13. T. Gerken, A. Lechleiter.
    Reconstruction of a Time-dependent Potential from Wave Measurements.
    Inverse Problems, Article ID 094001 33(9), IOPscience, 2017.

    Ausgezeichnet als Highlight Paper

    DOI: 10.1088/1361-6420/aa7e07
    online at: http://iopscience.iop.org/article/10.1088/1361-6420/aa7e07

14. A. Lechleiter.
    The Floquet-Bloch Transform and Scattering from Locally Perturbed Periodic Surfaces.
    Journal of Mathematical Analysis and Applications, 446(1):605-627, 2017.

    online at: http://arxiv.org/abs/1602.03349

15. S. Bosse, A. Lechleiter.
    A hybrid approach for structural monitoring with self-organizing multi-agent systems and inverse numerical methods in material-embedded sensor networks.
    Mechatronics, 34:12-37, 2016.

    DOI: 10.1016/j.mechatronics.2015.08.005
    online at: Link

16. E. Lakshtanov, A. Lechleiter.
    Difference Factorizations and Monotonicity in Inverse Medium Scattering for Contrasts with Fixed Sign on the Boundary .
    SIAM Journal on Mathematical Analysis, 48(6):3688-3707, SIAM, 2016.

    DOI: 10.1137/16M1060819
    online at: Link

17. Z. Jiang, H. Haddar, A. Lechleiter, M. El Guedri.
    Identification of magnetic deposits in 2-D axisymmetric eddy current models via shape optimization.
    Inverse Problems in Science and Engineering, 24(8):1385-1410, Taylor & Francis, 2016.

    DOI: 10.1080/17415977.2015.1110581
    online at: Link

18. A. Lechleiter, J. Schlasche.
    Identifying Lame Parameters from Time-dependent Elastic Wave Measurements.
    Inverse Problems in Science and Engineering, 25(1):2-26, 2016.

    DOI: 10.1080/17415977.2015.1132713

19. Z. Jiang, A. Lechleiter.
    Computing Interior Eigenvalues of Domains from Far Fields.
    IMA Journal of Numerical Analysis, 36:1452-1476, 2015.
20. A. Lechleiter, S. Peters.
    Determining transmission eigenvalues of anisotropic inhomogeneous media from far field data.
    Communications in Mathematical Sciences, 13(7), 1803 – 1827, International Press, Boston, Massachusetts, USA, 2015.

    DOI: 10.4310/CMS.2015.v13.n7.a8
    online at: http://www.intlpress.com/site/pub/pages/journals/items/cms/content/vols/0013/0007/a008/

21. T. Arens, A. Lechleiter.
    Indicator Functions for Shape Reconstruction Related to the Linear Sampling Method.
    SIAM Journal on Imaging Sciences, 8(1):513-535, SIAM, 2015.

    DOI: 10.1137/140965740

22. A. Lechleiter, M. Rennoch.
    Inside-outside duality and the determination of electromagnetic interior transmission eigenvalues.
    SIAM Journal on Mathematical Analysis, 47(1):684-705, SIAM, 2015.

    DOI: 10.1137/14098538X
    online at: Link

23. F. Miesner, A. Lechleiter, C. Müller.
    Reconstructing bottom water temperatures from measurements of temperature and thermal diffusivity in marine sediments.
    Ocean Science, 11:559-571, Copernicus Verlag, 2015.

    DOI: 10.5194/os-11-559-2015
    online at: Open Access via Ocean Science Homepage

24. A. Lechleiter, D. Nguyen.
    Scattering of Herglotz waves from periodic structures and mapping properties of the Bloch transform.
    Proceedings of the Royal Society of Edinburgh, Section: A Mathematics , 145(6):1283-1311, 2015.

    DOI: 10.1017/S0308210515000335

25. S. Peters, A. Lechleiter.
    The inside–outside duality for inverse scattering problems with near field data.
    Inverse Problems, 31(8), 085004, IOPscience, 2015.

    DOI: 10.1088/0266-5611/31/8/085004
    online at: http://iopscience.iop.org/0266-5611/31/8/085004/

26. A. Lechleiter.
    The MUSIC Algorithm for Impedance Tomography of Small Inclusions from Discrete Data.
    Inverse Problems, 31(9), 095004, IOPscience, 2015.

    DOI: 10.1088/0266-5611/31/9/095004
    online at: Link

27. P. Monk, A. Lechleiter.
    The Time Domain Lippmann-Schwinger Equation and Convolution Quadrature.
    Numerical Methods for Partial Differential Equations, 31(2):517-540, Wiley, 2015.

    DOI: 10.1002/num.21921
    online at: Link (arXiv)

28. A. Lechleiter, T. Rienmüller.
    Time-Harmonic Acoustic Wave Scattering in an Ocean with Depth-Dependent Sound Speed.
    Applicable Analysis - An International Journal, 95:978-999, 2015.

    DOI: 10.1080/00036811.2015.1047831

29. A. Lechleiter, D. Nguyen.
    A Trigonometric Galerkin Method for Volume Integral Equations Arising in TM Grating Scattering.
    Advances in Computational Mathematics, 40(1):1-25, Springer Verlag, 2014.

    DOI: 10.1007/s10444-013-9295-2
    online at: Link

30. H. Haddar, A. Lechleiter, S. Marmorat.
    An improved time domain linear sampling method for Robin and Neumann obstacles.
    Applicable Analysis - An International Journal, 93(2), 2014, Taylor & Francis, 2014.

    DOI: 10.1080/00036811.2013.772583
    online at: Link

31. A. Lechleiter, S. Peters.
    Analytical Characterization and Numerical Approximation of Interior Eigenvalues for Impenetrable Scatterers from Far Fields.
    Inverse Problems, 4(30), 045006, IOPscience, 2014.

    DOI: 10.1088/0266-5611/30/4/045006
    online at: Link

32. A. Lechleiter, H. Haddar, Z. Jiang.
    Artificial boundary conditions for axisymmetric eddy current probe problems.
    Computers & Mathematics with Applications, 68(12):1844-1870, 2014.

    DOI: doi:10.1016/j.camwa.2014.10.008
    online at: Link

33. T. Arens, K. Sandfort, S. Schmitt, A. Lechleiter.
    Analysing Ewald's method for the evaluation of Green's functions for periodic media.
    IMA Journal of Applied Mathematics, 78(3):405-431, 2013.

    DOI: 10.1093/imamat/hxr057
    online at: Link

34. A. Lechleiter, D. L. Nguyen.
    Factorization Method for Electromagnetic Inverse Scattering from Biperiodic Structures.
    SIAM Journal on Imaging Sciences, 6(2):1111-1139, SIAM, 2013.

    DOI: 10.1137/120903968
    online at: Link

35. A. Lechleiter, T. Rienmüller.
    Factorization Method for the Inverse Stokes Problem.
    Inverse Problems and Imaging, 7(4):1271-1293, 2013.

    DOI: doi:10.3934/ipi.2013.7.1271
    online at: Link

36. A. Lechleiter, D. L. Nguyen.
    On Uniqueness in Electromagnetic Scattering from Biperiodic Structures .
    ESAIM: Mathematical Modelling and Numerical Analysis, 47:1167-1184, 2013.

    DOI: 10.1051/m2an/2012063
    online at: Link

37. A. Kirsch, A. Lechleiter.
    The inside–outside duality for scattering problems by inhomogeneous media.
    Inverse Problems, 29(10), 104011, IOPscience, 2013.

    DOI: doi:10.1088/0266-5611/29/10/104011
    online at: Link

38. A. Lechleiter, K. Kazimierski, M. Karamehmedovic.
    Tikhonov regularization in L^p applied to inverse medium scattering.
    Inverse Problems, 29, 075003, IOPscience, 2013.

    DOI: doi:10.1088/0266-5611/29/7/075003
    online at: Link

39. A. Lechleiter, D. L. Nguyen.
    Volume Integral Equations for Scattering from Anisotropic Diffraction Gratings.
    Mathematical Methods in the Applied Sciences, 36(3), 262–274 pp., 2013.

    DOI: 10.1002/mma.2585
    online at: http://onlinelibrary.wiley.com/doi/10.1002/mma.2585/abstract

40. C. Bellis, A. Constantinescu, T. Coquet, T. Jaravel, A. Lechleiter.
    A non-iterative sampling approach using noise subspace projection for EIT .
    Inverse Problems, 28, 075015, IOPscience, 2012.

    DOI: doi:10.1088/0266-5611/28/7/075015
    online at: Link

41. A. Lechleiter, D. L. Nguyen.
    Spectral volumetric integral equation methods for acoustic medium scattering in a planar homogeneous 3D waveguide.
    IMA Journal of Numerical Analysis, 32(3):813-844, 2012.

    DOI: 10.1093/imanum/drr036
    online at: Link

42. T. Arens, D. Gintides, A. Lechleiter.
    Direct and inverse medium scattering in a 3D homogeneous planar waveguide.
    SIAM Journal on Applied Mathematics, 71:753-772, SIAM, 2011.

    DOI: 10.1137/100806333
    online at: http://dx.doi.org/10.1137/100806333

43. H. Haddar, A. Lechleiter.
    Electromagnetic wave scattering from rough penetrable layers.
    SIAM Journal on Mathematical Analysis, 43(5):2418-2443 , 2011.

    online at: http://dx.doi.org/10.1137/100783613

44. A. Lechleiter.
    Explicit characterization of the support of non-linear inclusions.
    Inverse Problems and Imaging, 5:675-694, 2011.

    DOI: 10.3934/ipi.2011.5.675
    online at: http://aimsciences.org/journals/displayArticlesnew.jsp?paperID=6426

45. Q. Chen, H. Haddar, A. Lechleiter, P. Monk.
    A Sampling Method for Inverse Scattering in the Time Domain.
    Inverse Problems, 26, 085001, IOPscience, 2010.

    DOI: 10.1088/0266-5611/26/8/085001
    online at: http://iopscience.iop.org/0266-5611/26/8/085001

46. A. Lechleiter, S. Ritterbusch.
    A variational method for scattering from penetrable rough layers.
    IMA Journal of Applied Mathematics, 75:366-391, 2010.

    DOI: 10.1093/imamat/hxp040
    online at: http://imamat.oxfordjournals.org/content/75/3/366

47. H. Haddar, A. Lechleiter.
    Asymptotic models for scattering problems from unbounded media with high conductivity.
    ESAIM: Mathematical Modelling and Numerical Analysis, 44:1295-1317, 2010.

    DOI: 10.1051/m2an/2010029
    online at: http://www.esaim-m2an.org/action/displayAbstract?fromPage=online&aid=8129349

48. A. Lechleiter.
    Imaging of Periodic Dielectrics.
    BIT Numerical Mathematics, 50:59-83, 2010.

    DOI: 10.1007/s10543-010-0255-7
    online at: http://www.springerlink.com/content/xt301t52307v6003/

49. A. Lechleiter, A. Rieder.
    Towards a general convergence theory for inexact Newton regularizations.
    Numerische Mathematik, 114:521-548, 2010.

    DOI: 10.1007/s00211-009-0256-0
    online at: http://www.springerlink.com/content/hg8n3tq067143166/

50. T. Arens, A. Lechleiter, D. R. . Luke .
    MUSIC for extended scatterers as an instance of the Factorization method.
    SIAM Journal on Applied Mathematics, 70:1283-1304, SIAM, 2009.

    DOI: 10.1137/080737836
    online at: http://dx.doi.org/10.1137/080737836

51. A. Lechleiter.
    The factorization method is independent of transmission eigenvalues.
    Inverse Problems and Imaging, 3:123-138, 2009.

    DOI: 10.3934/ipi.2009.3.123
    online at: http://www.aimsciences.org/journals/displayArticles.jsp?paperID=3966

52. T. Arens, A. Lechleiter.
    The linear sampling method revisited.
    Journal of Integral Equations and Applications, 21:179-202, 2009.

    DOI: 10.1216/JIE-2009-21-2-179
    online at: http://projecteuclid.org/euclid.jiea/1242652032

53. A. Kirsch, A. Lechleiter.
    The operator equations of Lippmann-Schwinger type for acoustic and electromagnetic scattering problems in L^2.
    Applicable Analysis - An International Journal, 88:807-830, 2009.

    DOI: 10.1080/00036810903042125
    online at: http://www.tandfonline.com/doi/abs/10.1080/00036810903042125

54. A. Lechleiter, A. Rieder.
    Newton regularizations for impedance tomography: convergence by local injectivity.
    Inverse Problems, 24, 065009, IOPscience, 2008.

    DOI: 10.1088/0266-5611/24/6/065009
    online at: http://iopscience.iop.org/0266-5611/24/6/065009

55. A. Lechleiter, N. Hyvönen, H. Hakula.
    The factorization method applied to the complete electrode model of impedance tomography.
    SIAM Journal on Applied Mathematics, 68:1097-1121, 2008.

    DOI: 10.1137/070683295
    online at: http://dx.doi.org/10.1137/070683295

56. T. Arens, D. Gintides, A. Lechleiter.
    Variational formulations for scattering in a 3-dimensional acoustic waveguide.
    Mathematical Methods in the Applied Sciences, 31:821-847, WILEY-VCH, 2008.

    DOI: 10.1002/mma.947
    online at: http://onlinelibrary.wiley.com/doi/10.1002/mma.947/abstract

57. A. Lechleiter.
    A regularization technique for the factorization method.
    Inverse Problems, 22:1605-1625, IOPscience, 2006.

    DOI: 10.1088/0266-5611/22/5/006
    online at: http://iopscience.iop.org/0266-5611/22/5/006/

58. A. Lechleiter, A. Rieder.
    Newton regularizations for impedance tomography: a numerical study.
    Inverse Problems, 22:1967-1987, IOPscience, 2006.

    DOI: doi:10.1088/0266-5611/22/6/004
    online at: http://iopscience.iop.org/0266-5611/22/6/004

Preprints (3)

1. A. Lechleiter.
   On the determination of sets supporting unknown sources for the wave equation from radiated fields.
   Zur Veröffentlichung eingereicht.

   online at: arxiv

2. A. Lechleiter, T. Rienmüller.
   Time-Harmonic Acoustic Wave Scattering in an Ocean with Depth-Dependent Sound Speed.
   Berichte aus der Technomathematik 15-01, Universität Bremen, 2015.
3. A. Lechleiter, D. Nguyen.
   Volume Integral Equation Methods for Scattering from Gratings: The TM Case.
   Berichte aus der Technomathematik 11-05, Universität Bremen, 2011.

Proceedings (2)

1. S. Bosse, A. Lechleiter.
   Structural Health and Load Monitoring with Material-embedded Sensor Networks and Self-organizing Multi-Agent Systems.
   SysInt - 2nd International Conference on System-integrated Intelligence, 02.07.2014-04.07.2014, Bremen, Germany.
   Procedia Technology, 15:669-691, 2014.

   online at: Link

2. A. Lechleiter, H. Haddar, Z. Jiang, M. El Guedri.
   Eddy current tomography of deposits in steam generators .
   19th European Signal Processing Conference (EUSIPCO 2011), August 29 - September 2, 2011, Barcelona, Spain.
   EUSPICO, pp. 2054-2058, 2011.

   online at: Link