arXiv subjects

Won-Kwang Park

Publications and source records attributed to Won-Kwang Park.

41 records · Page 3Linked to original sources

arXiv2012

Determination of the unknown support of thin penetrable inclusions within a half-space from multi-frequency response matrix

Thin, penetrable electromagnetic inclusions buried within a half space are retrieved from Multi-Static Response (MSR) matrix data collected above this half space at several frequencies. A non-iterative algorithm is proposed to that aim. It relies on the modeling of the MSR matrix according to a rigorous asymptotic expansion of the scattering amplitude. The supporting curves of single as well as multiple thin inclusions are retrieved in fairly good fashion. This is illustrated by a set of numerical inversions that are carried out from synthetic data, both noiseless and noisy ones.

math-ph↗

arXiv2012

Multi-frequency based location search algorithm of small electromagnetic inhomogeneities embedded in two-layered medium

In this paper, we consider a problem for finding the locations of electromagnetic inhomogeneities completely embedded in homogeneous two layered medium. For this purpose, we present a filter function operated at several frequencies and design an algorithm for finding the locations of such inhomogeneities. It is based on the fact that the collected Multi-Static Response (MSR) matrix can be modeled via a rigorous asymptotic expansion formula of the scattering amplitude due to the presence of such inhomogeneities. In order to show the effectiveness, we compare the proposed algorithm with traditional MUltiple SIgnal Classification (MUSIC) algorithm and Kirchhoff migration. Various numerical results demonstrate that the proposed algorithm is robust with respect to random noise and yields more accurate location than the MUSIC algorithm and Kirchhoff migration.

math-ph↗

arXiv2012

Fast shape reconstruction of perfectly conducting cracks by using a multi-frequency topological derivative strategy

This paper concerns a fast, one-step iterative technique of imaging extended perfectly conducting cracks with Dirichlet boundary condition. In order to reconstruct the shape of cracks from scattered field data measured at the boundary, we introduce a topological derivative-based electromagnetic imaging function operated at several nonzero frequencies. The properties of the imaging function are carefully analyzed for the configurations of both symmetric and non-symmetric incident field directions. This analysis explains why the application of incident fields with symmetric direction operated at multiple frequencies guarantees a successful reconstruction. Various numerical simulations with noise-corrupted data are conducted to assess the performance, effectiveness, robustness, and limitations of the proposed technique.

math-ph↗

arXiv2012

Multi-frequency topological derivative for approximate shape acquisition of curve-like thin electromagnetic inhomogeneities

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.

math-ph↗

arXiv2012

Multi-frequency imaging of perfectly conducting cracks via boundary measurements

Imaging of perfectly conducting crack(s) in a 2-D homogeneous medium using boundary data is studied. Based on the singular structure of the Multi-Static Response (MSR) matrix whose elements are normalized by an adequate test function at several frequencies, an imaging functional is introduced and analyzed. A non-iterative imaging procedure is proposed. Numerical experiments from noisy synthetic data show that acceptable images of single and multiple cracks are obtained.

math-ph↗