abbdd278_Es___Numerical_Methods_Seminar__TITLE
[DATE] 04/10/06 [SPEAKER] Fioralba Cakoni University of Delaware [TITLE] 
Title: Mixed boundary value problems in inverse electromagnetic scattering theory. We consider the inverse scattering problem of determining the shape and physical properties of an obstacle from a knowledge of the scattered field due to the scattering of an incident time-harmonic electromagnetic wave at fixed frequency. In particular, we discuss the linear sampling method for solving the inverse problem in the case of mixed boundary values problems for Maxwell equations. Mixed boundary value problems in electromagnetic scattering theory arise when the scattering object is a composite material such that parts of the scatterer have different electrical properties. Such objects can be partially coated perfect conductors or dielectrics, thin objects with one side a perfect conductor and the other side an imperfect conductor or dielectric. The mathematical analysis of the direct problem is difficult due to the non-standard solution space. Furthermore, no matter how smooth the boundary data is, the change of boundary conditions causes the scattered field to be singular at the interface, which gives rise to numerical difficulties. Concerning the corresponding inverse problem, since the physical structure of the composite medium is not known a priori, the use of weak scattering approximations and/or nonlinear optimization techniques are problematic. We will also discuss some related open problems and present examples of reconstruction showing the viability of our method for solving the inverse scattering problem.
CCMA PDEs & Numerical Methods Seminar
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