A Reduced Order Model Approach to Inverse Scattering in Lossy Layered Media

We introduce a reduced order model (ROM) methodology for inverse electromagnetic wave scattering in layered lossy media, using data gathered by an antenna which generates a probing wave and measures the time resolved reflected wave. We recast the wave propagation problem as a passive infinite-dimens...

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Bibliographic Details
Published in:Journal of scientific computing 2021-10, Vol.89 (1), p.1, Article 1
Main Authors: Borcea, Liliana, Druskin, Vladimir, Zimmerling, Jörn
Format: Article
Language:English
Subjects:
Algorithms
Antennas
Boundary conditions
Computational Mathematics and Numerical Analysis
Dynamical systems
Electric fields
Electrical resistivity
Electromagnetic radiation
Inverse problems
Inverse scattering
Linear algebra
Lossy media
Magnetic fields
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical models
Mathematics
Mathematics and Statistics
Ordinary differential equations
Parameter identification
Reduced order models
Reflected waves
Sparsity
Theoretical
Topical Collection dedicated to the ICERM Spring 2020 semester program on Model Order Reduction
Transfer functions
Wave propagation
Wave scattering
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Summary:We introduce a reduced order model (ROM) methodology for inverse electromagnetic wave scattering in layered lossy media, using data gathered by an antenna which generates a probing wave and measures the time resolved reflected wave. We recast the wave propagation problem as a passive infinite-dimensional dynamical system, whose transfer function is expressed in terms of the measurements at the antenna. The ROM is a low-dimensional dynamical system that approximates this transfer function. While there are many possible ROM realizations, we are interested in one that preserves passivity and in addition is: (1) data driven (i.e., is constructed only from the measurements) and (2) it consists of a matrix with special sparse algebraic structure, whose entries contain spatially localized information about the unknown dielectric permittivity and electrical conductivity of the layered medium. Localized means in the intervals of a special finite difference grid. The main result of the paper is to show with analysis and numerical simulations that these unknowns can be extracted efficiently from the ROM.
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-021-01616-7