Investigation of a non-iterative technique based on topological derivatives for fast localization of small conductivity inclusions. (15th August 2022)

• Record Type: Journal Article
• Authors: Park, Won-Kwang
• Is Part Of: Computers & mathematics with applications. Volume 120(2022)
• Page Start: 45
• Page End: 59
• Publication Date: 2022-08-15
• Subjects: Topological derivative -- Inverse conductivity problem -- Asymptotic formula -- Numerical simulation; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2022.06.022
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this contribution, we consider a topological derivative-based non-iterative technique for an inverse conductivity problem of localizing a small-conductivity inclusion completely embedded in a homogeneous domain via boundary measurement data. For this purpose, we derive the topological derivative by applying an asymptotic formula in the presence of a small-diameter conductivity inclusion and establish a mathematical structure of topological derivative. On the basis of the established structure, we propose a new imaging function with appropriate boundary conditions. Results of numerical simulation are presented to show the feasibility and limitations of the designed imaging function.