14 research outputs found
Reconstruction of the refractive index from experimental backscattering data using a globally convergent inverse method
The problem to be studied in this work is within the context of coefficient
identification problems for the wave equation. More precisely, we consider the
problem of reconstruction of the refractive index (or equivalently, the
dielectric constant) of an inhomogeneous medium using one backscattering
boundary measurement. The goal of this paper is to analyze the performance of a
globally convergent algorithm of Beilina and Klibanov on experimental data
acquired in the Microwave Laboratory at University of North Carolina at
Charlotte. The main challenge working with experimental data is the the huge
misfit between these data and computationally simulated data. We present data
pre-processing steps to make the former somehow look similar to the latter.
Results of both non-blind and blind targets are shown indicating good
reconstructions even for high contrasts between the targets and the background
medium.Comment: 25 page
Computational design of nanophotonic structures using an adaptive finite element method
We consider the problem of the construction of the nanophotonic structures of
arbitrary geometry with prescribed desired properties. We reformulate this
problem as an optimization problem for the Tikhonov functional which is
minimized on adaptively locally refined meshes. These meshes are refined only
in places where the nanophotonic structure should be designed. Our special
symmetric mesh refinement procedure allows the construction of different
nanophotonic structures. We illustrate efficiency of our adaptive optimization
algorithm on the construction of nanophotonic structure in two dimensions
Application of the Finite Element Method in a Quantitative Imaging technique
We present the Finite Element Method (FEM) for the numerical solution of the
multidimensional coefficient inverse problem (MCIP) in two dimensions. This
method is used for explicit reconstruction of the coefficient in the hyperbolic
equation using data resulted from a single measurement. To solve our MCIP we
use approximate globally convergent method and then apply FEM for the resulted
equation. Our numerical examples show quantitative reconstruction of the sound
speed in small tumor-like inclusions
Reconstruction of shapes and refractive indices from backscattering experimental data using the adaptivity
We consider the inverse problem of the reconstruction of the spatially
distributed dielectric constant $\varepsilon_{r}\left(\mathbf{x}\right), \
\mathbf{x}\in \mathbb{R}^{3}n\left(\mathbf{x}\right) =\sqrt{\varepsilon_{r}\left(\mathbf{x}\right)}.\varepsilon_{r}\left(\mathbf{x}\right) $ is reconstructed using a
two-stage reconstruction procedure. In the first stage an approximately
globally convergent method proposed is applied to get a good first
approximation of the exact solution. In the second stage a locally convergent
adaptive finite element method is applied, taking the solution of the first
stage as the starting point of the minimization of the Tikhonov functional.
This functional is minimized on a sequence of locally refined meshes. It is
shown here that all three components of interest of targets can be
simultaneously accurately imaged: refractive indices, shapes and locations
Reconstruction from blind experimental data for an inverse problem for a hyperbolic equation
We consider the problem of reconstruction of dielectrics from blind
backscattered experimental data. Experimental data were collected by a device,
which was built at University of North Carolina at Charlotte. This device sends
electrical pulses into the medium and collects the time resolved backscattered
data on a part of a plane. The spatially distributed dielectric constant
is the unknown
coefficient of a wave-like PDE. This coefficient is reconstructed from those
data in blind cases. To do this, a globally convergent numerical method is
used.Comment: 27 page