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Publikationen der AG Inverse Probleme

Zeitschriftenartikel (59)

  1. B. Zhang, R. Zhang.
    A New Integral Equation Formulation for Scattering by Penetrable Diffraction Gratings.
    Journal of Computational Mathematics, 36(1):110-127, 2018.

    online unter: http://www.global-sci.org/jcm/galley/JCM2016-0501.pdf

  2. 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 S., 2017.

    DOI: 10.1137/16M1067524
    online unter: Arxiv

  3. 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 unter: http://epubs.siam.org/doi/pdf/10.1137/16M1104111

  4. 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
    online unter: http://www.sciencedirect.com/science/article/pii/S0021999117301985

  5. A. Lechleiter, T. Rienmüller.
    Collocation discretization for an integral equation in ocean acoustics with depth-dependent speed of sound.
    Erscheint in Mathematical Methods in the Applied Sciences

    DOI: 10.1002/mma.4082

  6. M. Li, R. Zhang.
    Near-field imaging of sound-soft obstacles in periodic waveguides .
    Inverse Problems and Imaging, 11(6):1091-1105, 2017.

    online unter: https://aimsciences.org/journals/displayArticlesnew.jsp?paperID=14621

  7. 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
    online unter: Link

  8. 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 unter: https://doi.org/10.1016/j.camwa.2017.08.042

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

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

  10. 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 unter: http://arxiv.org/abs/1602.03349

  11. 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 unter: Link

  12. G. Sun, R. Zhang.
    A sampling method for the reconstruction of a periodic interface in a layered medium.
    Inverse Problems, 075005 32(7), 2016.

    DOI: https://doi.org/10.1088/0266-5611/32/7/075005
    online unter: https://doi.org/10.1088/0266-5611/32/7/075005

  13. 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 unter: Link

  14. 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 unter: Link

  15. 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

  16. S. Peters, A. Kleefeld.
    Numerical Computations of Interior Transmission Eigenvalues for Scattering Objects with Cavities.
    Inverse Problems, 32(4), IOPscience, 2016.

    DOI: 10.1088/0266-5611/32/4/045001
    online unter: http://iopscience.iop.org/article/10.1088/0266-5611/32/4/045001/meta

  17. C. Müller, F. Miesner, R. Usbeck.
    Temperatures in shallow marine sediments: Influence of thermal properties, seasonal forcing, and man-made heat sources.
    Erscheint in Applied Thermal Engineering

    DOI: doi:10.1016/j.applthermaleng.2016.07.105
    online unter: http://www.sciencedirect.com/science/article/pii/S1359431116312364

  18. S. Peters.
    The Inside-Outside Duality for Elastic Scattering Problems.
    Applicable Analysis - An International Journal, 96(1):48-69, 2016.

    DOI: 10.1080/00036811.2016.1210789
    online unter: http://www.tandfonline.com/doi/full/10.1080/00036811.2016.1210789

  19. J. Li, G. Sun, R. Zhang.
    The numerical solution of scattering by infinite rough interfaces based on the integral equation method.
    Computers & Mathematics with Applications, 71(7):1491-1502, 2016.

    online unter: https://ac.els-cdn.com/S0898122116300852/1-s2.0-S0898122116300852-main.pdf?_tid=83195944-b405-11e7-9068-00000aacb362&acdnat=1508332323_96d55a6d6c1263aa0750f01fce4f380f

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

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

  22. 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

  23. 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 unter: Link

  24. 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 unter: Open Access via Ocean Science Homepage

  25. 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

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

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

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

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

  28. 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 unter: Link (arXiv)

  29. 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

  30. 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 unter: Link

  31. 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 S., Taylor & Francis, 2014.

    DOI: 10.1080/00036811.2013.772583
    online unter: Link

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

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

  33. 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 unter: Link

  34. 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 unter: Link

  35. 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 unter: Link

  36. 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 unter: Link

  37. 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 unter: Link

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

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

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

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

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

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

  41. 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 S., IOPscience, 2012.

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

  42. 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 unter: Link

  43. 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 unter: http://dx.doi.org/10.1137/100806333

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

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

  45. 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 unter: http://aimsciences.org/journals/displayArticlesnew.jsp?paperID=6426

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

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

  47. 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 unter: http://imamat.oxfordjournals.org/content/75/3/366

  48. 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 unter: http://www.esaim-m2an.org/action/displayAbstract?fromPage=online&aid=8129349

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

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

  50. 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 unter: http://www.springerlink.com/content/hg8n3tq067143166/

  51. 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 unter: http://dx.doi.org/10.1137/080737836

  52. 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 unter: http://www.aimsciences.org/journals/displayArticles.jsp?paperID=3966

  53. 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 unter: http://projecteuclid.org/euclid.jiea/1242652032

  54. 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 unter: http://www.tandfonline.com/doi/abs/10.1080/00036810903042125

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

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

  56. 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 unter: http://dx.doi.org/10.1137/070683295

  57. 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 unter: http://onlinelibrary.wiley.com/doi/10.1002/mma.947/abstract

  58. 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 unter: http://iopscience.iop.org/0266-5611/22/5/006/

  59. 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 unter: http://iopscience.iop.org/0266-5611/22/6/004

Tagungsbeiträge (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, Deutschland.
    Procedia Technology, 15:669-691, 2014.

    online unter: 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, Spanien.
    EUSPICO, S. 2054-2058, 2011.

    online unter: Link

Buchkapitel (2)

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

    online unter: Link

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

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

Qualifikationsarbeiten (3)

  1. M. Rennoch.
    Regularization Methods in Banach Spaces Applied to Inverse Medium Scattering Problems.
    Dissertationsschrift, Universität Bremen, 2017.

    online unter: Elektronische Bibliothek der Universität Bremen

  2. S. Peters.
    The Inside-Outside Duality in Inverse Scattering Theory.
    Dissertationsschrift, Universität Bremen, 2016.

    online unter: http://nbn-resolving.de/urn:nbn:de:gbv:46-00105263-13

  3. T. Rienmüller.
    Integral Equation Methods for Ocean Acoustics with Depth-Dependent Background Sound Speed.
    Dissertationsschrift, Universität Bremen, 2015.

Preprints (7)

  1. R. Zhang.
    A High Order Numerical Method for Scattering from Locally Perturbed Periodic Surfaces.
    Zur Veröffentlichung eingereicht.

    online unter: https://arxiv.org/pdf/1708.07870.pdf

  2. F. Bürgel, K. Kazimierski, A. Lechleiter.
    IPscatt—a MATLAB Toolbox for the Inverse Medium Problem in Scattering.
    Zur Veröffentlichung eingereicht.
  3. A. Lechleiter, R. Zhang.
    Reconstruction of Local Perturbations in Periodic.
    Zur Veröffentlichung eingereicht.

    online unter: https://arxiv.org/pdf/1709.09166.pdf

  4. R. Zhang.
    The Study of the Bloch Transformed Total Fields of the Scattering Problems with Locally Perturbed Periodic Surfaces.
    Zur Veröffentlichung eingereicht.

    online unter: https://arxiv.org/pdf/1708.07560.pdf

  5. M. Rennoch.
    Non-linear Tikhonov Regularization in Banach Spaces for Inverse Electromagnetic Scattering from Anisotropic Penetrable Non-Magnetic Media.
    Zur Veröffentlichung eingereicht.
  6. A. Lechleiter.
    On the determination of sets supporting unknown sources for the wave equation from radiated fields.
    Zur Veröffentlichung eingereicht.

    online unter: arxiv

  7. 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.