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