Inside-Outside Duality and Non-Destructive Testing

This project considers the characterization of defaults in materials by measuring scattered waves. The special relation between defects and measurements we want to exploit is a link between interior resonances of the defects (or inhomogeneities) and the eigenvalues of the measurement operator. This link is called Inside-Outside Duality. We hope to be able to use it for the improvement of identification techniques for non-destructive testing. 

Publications

1. 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

2. 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

3. 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/

4. 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

5. 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

6. Z. Jiang, A. Lechleiter.
   Computing Interior Eigenvalues of Domains from Far Fields.
   IMA Journal of Numerical Analysis, 36:1452-1476, 2015.
7. 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

8. 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