Inverse medium scattering for the Helmholtz equation at fixed frequency
نویسندگان
چکیده
Consider a time-harmonic electromagnetic plane wave incident on a medium enclosed by a bounded domain in R2. In this paper, existence and uniqueness of the variational problem for the direct scattering are established. An energy estimate for the scattered field is obtained on which the Born approximation is based. The Fréchet differentiability of the scattering map is examined. A new continuation method for the inverse medium scattering, which reconstructs the scatterer of an inhomogeneous medium from the boundary measurements of the scattered waves, is developed. The algorithm requires only single-frequency scattering data. Using an initial guess from the Born approximation, each update is obtained via recursive linearization on the spatial frequency of a one-parameter family of plane waves by solving one forward and one adjoint problem of the Helmholtz equation. (Some figures in this article are in colour only in the electronic version)
منابع مشابه
Computational Inverse Medium Scattering at Fixed Frequency
A continuation method is presented for solving the inverse medium scattering problem of the Helmholtz equation in R. The algorithm requires only single-frequency scattering data. Using an initial guess from the Born approximation, each update is obtained via recursive linearization on the spatial frequency of a one-parameter family of plane waves by solving one forward and one adjoint problem o...
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