A robust approach with numerical demonstrations for the inverse scattering problem using a Carleman contraction map
arxiv(2024)
摘要
This paper addresses the inverse scattering problem in the domain Omega. The
input data, measured outside Omega, involve the waves generated by the
interaction of plane waves with various directions and unknown scatterers fully
occluded inside Omega. The output of this problem is the spatially dielectric
constant of these scatterers. Our approach to solving this problem consists of
two primary stages. Initially, we eliminate the unknown dielectric constant
from the governing equation, resulting in a system of partial differential
equations. Subsequently, we develop the Carleman contraction mapping method to
effectively tackle this system. It is noteworthy to highlight this method's
robustness. It does not request a precise initial guess of the true solution,
and its computational cost is not expensive. Some numerical examples are
presented.
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