Unit:
Κατεύθυνση Εφαρμοσμένα ΜαθηματικάLibrary of the School of Science
Supervisors info:
Ευαγγελία Κόττα-Αθανασιάδου, Επίκουρη Καθηγήτρια, Τμήμα Μαθηματικών, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών.
Original Title:
The Ellipsoidal Harmonics in Solving Inverse Scattering Problems
Translated title:
The Ellipsoidal Harmonics in Solving Inverse Scattering Problems
Summary:
The main subject of this study is the solution of inverse acoustic and electromagnetic scattering problems for ellipsoids using the ellipsoidal harmonics. The scattering problems of time-harmonic acoustic and electromagnetic plane waves by an ellipsoidal scatterer for various boundary conditions imposed on its surface are considered. The study of the ellipsoidal coordinate system, leads to the definition of the ellipsoidal harmonics, which enter in the scattering problems via the low-frequency theory. The methodology which leads to the derivation of low-frequency approximations for ellipsoids is presented. Inverse scattering problems for acoustic and electromagnetic waves for an ellipsoidal scatterer are described. A finite number of measurements of far-field data or near-field data leads to the specification of the size and the orientation of an unknown ellipsoidal scatterer. For the case of penetrable scatterer, physical parameters of its interior are also obtained. Corresponding results for the cases of the sphere and the spheroid are derived, considering them as geometrically degenerate cases of the ellipsoid for appropriate values of its geometrical parameters.
Main subject category:
Science
Keywords:
Scattering, ellipsoidal harmonics, inverse scattering problems, ellipsoidal scatterer
