Premium
The interior transmission problem for anisotropic Maxwell's equations and its applications to the inverse problem
Author(s) -
Haddar Houssem
Publication year - 2004
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.465
Subject(s) - inverse scattering problem , maxwell's equations , inverse problem , operator (biology) , anisotropy , characterization (materials science) , mathematical analysis , field (mathematics) , range (aeronautics) , scattering , transmission (telecommunications) , inverse , physics , mathematics , optics , computer science , geometry , pure mathematics , telecommunications , materials science , biochemistry , chemistry , repressor , transcription factor , composite material , gene
The interior transmission problem appears naturally in the study of the inverse scattering problem of determining the shape of a penetrable medium from a knowledge of the time harmonic incident waves and the far field patterns of the scattered waves. We propose a variational study of this problem in the case of Maxwell's equations in an inhomogeneous anisotropic medium. Then we apply the obtained results to build an ‘extented far field’ operator and give a characterization of the medium from the knowledge of the range of this operator. We then show how the linear sampling method can be viewed as an approximation of this characterization. Copyright © 2004 John Wiley & Sons, Ltd.