An adaptive finite element/finite difference domain decomposition method for applications in microwave imaging

TL;DR

This paper introduces an adaptive domain decomposition method combining finite element and finite difference techniques for Maxwell's equations, enabling improved dielectric permittivity reconstruction in microwave imaging.

Contribution

It presents a novel adaptive domain decomposition approach with optimization-based reconstruction algorithms and mesh refinement for microwave imaging applications.

Findings

Qualitative reconstruction of dielectric permittivity in breast phantom

Effective adaptive algorithms for improved accuracy

Mesh refinement indicators enhance reconstruction quality

Abstract

A new domain decomposition method for Maxwell's equations in conductive media is presented. Using this method reconstruction algorithms are developed for determination of dielectric permittivity function using time-dependent scattered data of electric field. All reconstruction algorithms are based on optimization approach to find stationary point of the Lagrangian. Adaptive reconstruction algorithms and space mesh refinement indicators are also presented. Our computational tests show qualitative reconstruction of dielectric permittivity function using anatomically realistic breast phantom.