Veranstaltungsarchiv
Seminar in Analysis und Numerik
Larisa Beilina: Reconstruction of dielectrics from experimental data via a hybrid globally convergent/adaptive inverse alogrithm
abstract: In [1] a globally convergent numerical method for a Coefficient Inverse Problems (CIP) for a hyperbolic PDE was developed. Next, a two-stage numerical procedure was proposed in [2,3,4]. In this procedure the technique of [1] is used as the first stage. Next, the Adaptive Finite Element method is used as the second stage for the refinement. In [5] the first stage was verified on blind experimental data. The goal of the current publication is to demonstrate that the two-stage numerical procedure
applied to the same experimental data can significantly improve imaging results compared with the first stage only. Specifically, we now accurately reconstruct not only locations and refractive indices of dielectric abnormalities, as it was in [5], but their shapes as well. The analytical part of this talk will be focused on two recommendations for the mesh refinement in a posteriori error analysis for the adaptivity technique.
[1] Beilina, L.; Klibanov, M. V.; 2008: A globally convergent numerical method for a coefficient inverse problem; SIAM J. Sci. Comp., 31, 478-509
[2] Beilina, L.; Klibanov, M. V.; 2010: Synthesis of global convergence and adaptivity for a hyperbolic coefficient inverse problem in 3D; J. Inverse and Ill-posed Problems, 18, 85-132
[3] Beilina, L.; Klibanov, M. V.; 2010: A posteriori error estimates for the adaptivity technique for the Tikhonov functional and global convergence for a coefficient inverse problem; Inverse Problems, 26, 045012
[4] Beilina, L.; Klibanov, M. V.; Kokurin, M. Yu; 2010: Adaptivity with relaxation for ill-posed problems and global convergence for a coefficient inverse problem; Journal of Mathematical Sciences, Springer, 167, 279-325
[5] Klibanov, M. V.; Fiddy, M. A.; Beilina, L.; Pantong, N.; Schenk, J.; 2010: Picosecond scale experimental verification of a globally convergent numerical method for a coefficient inverse problem, Inverse Problems, 26, 045003, 2010.
Freitag, 19. 11. 2010, 9.00 Uhr
im Grossen Hörsaal
Mathematisches Institut
Rheinsprung 21, Basel