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

TL;DR

This paper presents a fast, one-step multi-frequency topological derivative method for reconstructing the shape of perfectly conducting cracks from boundary measurements, with analysis and numerical validation demonstrating robustness and effectiveness.

Contribution

It introduces a novel multi-frequency topological derivative approach for crack imaging, providing a detailed analysis of its properties and advantages over single-frequency methods.

Findings

Effective reconstruction with multiple frequencies

Robustness against noise demonstrated

Analysis explains success with symmetric incident fields

Abstract

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.