Reconstruction of obstacles embedded in waveguides. (English) Zbl 1281.78013
Li, Jichun (ed.) et al., Recent advances in scientific computing and applications. Eighth international conference on scientific computing and applications, University of Nevada, Las Vegas, NV, USA, April 1–4, 2012. Proceedings. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-8737-0/hbk; 978-0-8218-9501-6/ebook). Contemporary Mathematics 586, 341-350 (2013).
Summary: The reconstruction of obstacles embedded in a periodic waveguide with arbitrary geometry is considered. The measurement is on a line segment of the scattered field due to point sources inside the waveguide. A linear sampling type method is proposed to characterize the obstacles using the solutions of the near field ill-posed linear integral equations. Due to the fact that we consider waveguides with arbitrary geometry to compute the background Green’s function, we employ a method based on the limiting absorption principle and the recursive doubling technique. Furthermore, an algorithm is proposed to speed up the sampling procedure. Numerical examples are presented to demonstrate the performance of the proposed method.
For the entire collection see [Zbl 1264.65002].
For the entire collection see [Zbl 1264.65002].
MSC:
| 78A46 | Inverse problems (including inverse scattering) in optics and electromagnetic theory |
| 35R30 | Inverse problems for PDEs |
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
| 35P25 | Scattering theory for PDEs |
| 78A50 | Antennas, waveguides in optics and electromagnetic theory |
| 78A45 | Diffraction, scattering |
