Topological derivative strategy for one-step iteration imaging of arbitrary shaped thin, curve-like electromagnetic inclusions

Authors:
Won-Kwang Park
Affiliations:
Department of Mathematics, Kookmin University, Seoul 136-702, Republic of Korea
Venue:
Journal of Computational Physics
Year:
2012

Citing 6
Cited 1

On the Topological Derivative in Shape Optimization

SIAM Journal on Control and Optimization
MUSIC-Type Electromagnetic Imaging of a Collection of Small Three-Dimensional Inclusions

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Crack reconstruction using a level-set strategy

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Electromagnetic MUSIC-type imaging of perfectly conducting, arc-like cracks at single frequency

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Asymptotic Imaging of Perfectly Conducting Cracks

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Stability and Resolution Analysis for a Topological Derivative Based Imaging Functional

SIAM Journal on Control and Optimization

Analysis of a multi-frequency electromagnetic imaging functional for thin, crack-like electromagnetic inclusions

Applied Numerical Mathematics

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Abstract

In this manuscript, a fast imaging of thin, curve-like electromagnetic inclusions completely hidden in the homogeneous domain with smooth boundaries is considered. By creating an electromagnetic inclusion of a small diameter and applying the asymptotic expansion formula in the existence of such an inclusion, the topological derivative is successfully derived. Based on this derivative, a one-step iteration imaging algorithm is designed by solving an adjoint problem. Various numerical experiments of single and multiple inclusions demonstrate the viability and limitation of the designed algorithm.