Inside-Outside Duality and Non-Destructive Testing
Working Group: | Former WG Inverse Problems |
Leadership: | Prof. Dr. Armin Lechleiter |
Processor: | Dr. Stefan Peters |
Funding: | Exzellenzinitiative Uni Bremen - Explorationsprojekt M4 |
Project partner: | |
Time period: | 01.07.2013 - 30.06.2016 |
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
- 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 - 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. - 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/ - 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 - 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
- Z. Jiang, A. Lechleiter.
Computing Interior Eigenvalues of Domains from Far Fields.
IMA Journal of Numerical Analysis, 36:1452-1476, 2015. - 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 - 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