T. Le, V. A. Khoa, M. V. Klibanov, L. H. Nguyen, G. W. Bidney, V. N. Astratov
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Numerical Verification of the Convexification Method for a Frequency-Dependent Inverse Scattering Problem with Experimental Data
Abstract
The reconstruction of physical properties of a medium from boundary measurements,
known as inverse scattering problems, presents significant challenges. The present study aims to
validate a newly developed convexification method for a 3D coefficient inverse problem in the case
of buried unknown objects in a sandbox, using experimental data collected by a microwave
scattering facility at The University of North Carolina at Charlotte. Our study considers the
formulation of a coupled quasilinear elliptic system based on multiple frequencies. The system can
be solved by minimizing a weighted Tikhonov-like functional, which forms our convexification
method. Theoretical results related to the convexification are also revisited in this work.
期刊介绍：
Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.
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