2012/07/17 by Won‐Kwang Park, Won-Kwang Park · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Algorithm #Artificial intelligence #Computer science #Derivative (finance) #Dielectric #Embedding #Fréchet derivative #Geometry #Geophysical Methods and Applications #Mathematical analysis #Mathematics #Numerical methods in inverse problems #Permittivity #Physics #Structural Health Monitoring Techniques #Topology (electrical circuits) #math-ph #math.MP
paper · pdf · doi:10.1016/j.jmaa.2013.03.040
published as J. Math. Anal. Appl., 402 (2013), 501-518 · 25 pages, 28 figures
arxiv created 2012/07/17 · openalex publication_date 2013/03/22 · arxiv updated 2013/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper, we investigate a non-iterative imaging algorithm based on the topological derivative in order to retrieve the shape of penetrable electromagnetic inclusions when their dielectric permittivity and/or magnetic permeability differ from those in the embedding (homogeneous) space. The main objective is the imaging of crack-like thin inclusions, but the algorithm can be applied to arbitrarily shaped inclusions. For this purpose, we apply multiple time-harmonic frequencies and normalize the topological derivative imaging function by its maximum value. In order to verify its validity, we apply it for the imaging of two-dimensional crack-like thin electromagnetic inhomogeneities completely hidden in a homogeneous material. Corresponding numerical simulations with noisy data are performed for showing the efficacy of the proposed algorithm.