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Institute for Applied and Numerical Mathematics
Research Group 4: Inverse Problems
PD Dr. Tilo Arens
Publications

Publications

Textbooks

  1. T. Arens, R. Busam, F. Hettlich, C. Karpfinger and H.Stachel, Grundwissen Mathematikstudium, Spektrum Akademischer Verlag, 2013.
  2. T. Arens, F. Hettlich, C. Karpfinger, U.Kockelkorn, K.Lichtenegger and H.Stachel, Mathematik, Spektrum Akademischer Verlag, 2008.

Theses

  1. Scattering by Biperiodic Layered Media: The Integral Equation Approach, Habilitation thesis, Karlsruhe Institute of Technology, 2010.
  2. The scattering of elastic waves by rough surfaces, PhD thesis, Brunel University, 2000.

Preprints

  1. T. Arens, F. Hagemann, and F. Hettlich. On potential-based shape derivatives of the electromagnetic transmission problem. CRC 1173 Preprint 2022/75, Karlsruhe Institute of Technology, December 2022.
  2. T. Arens, M. Knöller, and R. Schurr. Inverse electromagnetic scattering problems for long tubular objects. CRC 1173 Preprint 2024/17, Karlsruhe Institute of Technology, August 2024. Codes available at https://doi.org/10.35097/9q92k9up08vnt4q7.

Journal Articles

  1. T. Arens, R. Zhang. A nonuniform mesh method in the Floquet parameter domain for wave scattering by periodic surfaces. Math. Meth. Appl. Sci. 48 (2025), 4289-4309. http://doi.org/10.1002/mma.10548.
  2. T. Arens, N. Shafieeabyaneh, and R. Zhang. A high-order numerical method for solving non-periodic scattering problems in three-dimensional bi-periodic structures. Z. Ang. Math. Mech. 104, e202300650 (2024), https://doi.org/10.1002/zamm.202300650.
  3. T. Arens, R. Griesmaier, and R. Zhang. Monotonicity-based shape reconstruction for an inverse scattering problem in a waveguide. Inverse Problems 39 (7), 075009 (2023). DOI: https://doi.org/10.1088/1361-6420/acd4e0.
  4. X. Garcia-Santiago, M. Hammerschmidt, J. Sachs, S. Burger, H. Kwon, M. Knöller, T. Arens, P. Fischer, I. Fernandez-Corbaton, and C. Rockstuhl. Toward maximally electromagnetically chiral scatterers at optical frequencies. ACS Photonics, 9 (6), 1954–1964, (2022). DOI: https://doi.org/10.1021/acsphotonics.1c01887.
  5. T. Arens, R. Griesmaier and Marvin Knöller. Maximizing the electromagnetic chirality of thin dielectric tubes. SIAM J. Appl. Math. 81, 1979–2006 (2021), DOI: https://epubs.siam.org/doi/10.1137/21M1393509.
  6. T. Arens, X. Ji, and X. Liu. Inverse electromagnetic obstacle scattering problems with multi-frequency sparse backscattering far field data. Inverse Problems 36, 105007 (2020), DOI: 10.1088/1361-6420/abb5e2.
  7. F. Z. Goffi, K. Lemrabet, and T. Arens. Approximate impedance for time-harmonic Maxwell's equations in a non planar domain with contrasted multi-thin layers. Journal of Mathematical Analysis and Applications 489, 124141 (2020), DOI: https://doi.org/10.1016/j.jmaa.2020.124141.
  8. F. Hagemann, T. Arens, T. Betcke, F. Hettlich, Solving inverse electromagnetic scattering problems via domain derivatives, Inverse Problems 35, 084005 (2019), DOI: 10.1088/1361-6420/ab10cb.
  9. T. Arens, F. Hagemann, F. Hettlich, A. Kirsch, The Definition and Measurement of Electromagnetic Chirality, Math. Meth. Appl. Sci. 41, 559-572 (2018), DOI: 10.1002/mma.4628.
  10. T. Arens, J. Sylvester, Born Non-Scattering Electromagnetic Media, Journal of Inverse and Ill-Posed Problems 25, 469-482 (2017), DOI: 10.1515/jiip-2016-0054.
  11. T. Arens, T. Rösch, A collocation method for weakly singular integral equations with super-algebraic convergence rate, Numer. Math. 134, 441-472 (2016), DOI 10.1007/s00211-015-0783-9.
  12. T. Arens, A. Lechleiter, Indicator Functions for Shape Reconstruction Related to the Linear Sampling Method, SIAM J. Imag. Sci. 8, 513-535 (2015).
  13. T. Arens, K. Sandfort, S. Schmitt and A. Lechleiter, Analysing Ewald's Method for the Evaluation of Green's Functions for Periodic Media, IMA J. Appl. Math. 78, 405-431 (2013), DOI: https://doi.org/10.1093/imamat/hxr057.
  14. T. Arens, D. Gintides und A. Lechleiter, Direct and Inverse Medium Scattering in a Three-Dimensional Homogeneous Planar Waveguide, SIAM J. Appl. Math. 71, 753-772 (2011), doi: 10.1137/100806333
  15. T. Arens, A. Lechleiter and R.L. Luke, MUSIC for Extended Scatterers as an Instance of the Factorization Method, SIAM J. Appl. Math. 70, 1283-1304 (2009).
  16. T. Arens and A. Lechleiter, The Linear Sampling Method Revisited, J. Int. Equ. Appl. 21, 179-202 (2009).
  17. T. Arens, D. Gintides and A. Lechleiter, Variational Formulations for Scattering in a 3-Dimensional Acoustic Waveguide, Math. Meth. Appl. Sci. 31, 821-847 (2008).
  18. T. Arens, S.N. Chandler-Wilde and J.A. DeSanto, On integral equation and least squares methods for scattering by diffraction gratings, Communications in Computational Physics 1, 1010-1042 (2006).
  19. T. Arens and T. Hohage , On radiation conditions for rough surface scattering problems, IMA J. Appl. Math 70, 839-847 (2005).
  20. T. Arens and N. Grinberg , A complete Factorization Method for scattering by periodic surfaces, Computing 75, 111-132 (2005).
  21. T. Arens, Why Linear Sampling works! Inverse Problems 20, 163-173 (2004).
  22. D. Natroshvili, T. Arens and S.N. Chandler-Wilde, Uniqueness, existence and integral equation formulations for interface scattering problems, Memoirs on Differential Equations and Mathematical Physics 30, Georgian Academy of Sciences, 105-146 (2003).
  23. T. Arens and A. Kirsch, The factorization method in inverse scattering from periodic structures, Inverse Problems 19, 1195-1211 (2003).
  24. T. Arens, S.N. Chandler-Wilde and K. Haseloh, Solvability and spectral properties of integral equations on the real line: II. $L^p$ spaces and applications, J. Int. Equ. Appl. 15, 1-35 (2003).
  25. T. Arens, An approximation property of elastic Herglotz wave functions and its application in the Linear Sampling method, Journal of Ill-Posed and Inverse Problems 11, 219-233 (2003).
  26. T. Arens, S.N. Chandler-Wilde and K. Haseloh, Solvability and spectral properties of integral equations on the real line: I. Weighted spaces of continuous functions, J. Math. Anal. Appl. 272, 276-302 (2002).
  27. T. Arens, Existence of solution in elastic wave scattering by unbounded rough surfaces, Math. Meth. Appl. Sci. 25, 507-528 (2002).
  28. T. Arens, Uniqueness for elastic wave scattering by rough surfaces, SIAM J. Math. Anal. 33, 461-476 (2001).
  29. T. Arens, Linear sampling methods for 2D inverse elastic wave scattering, Inverse Problems 17, 1445--1464 (2001).
  30. A. Meier, T. Arens, S.N. Chandler-Wilde and A. Kirsch, A Nyström method for a class of integral equations on the real line with applications to scattering by diffraction gratings and rough surfaces, J. Int Equ. Appl. 12, 281-321 (2000).
  31. T. Arens, The scattering of plane elastic waves by a one-dimensional periodic surface, Math. Meth. Appl. Sci. 22, 55--72 (1999).
  32. T. Arens, A new integral equation formulation for the scattering of plane elastic waves by diffraction gratings, J. Int. Equ. Appl. 11, 275-297 (1999).