arXiv subjects

Eric Lindström

Publications and source records attributed to Eric Lindström.

6 recordsLinked to original sources

arXiv2026

Variational optimization approach for reconstruction of dielectric permittivity and conductivity functions using partial boundary measurements

We present a variational optimization approach for the solution of a coefficient inverse problem of simultaneous reconstruction of the dielectric permittivity and conductivity functions in time-dependent Maxwell's system using limited boundary observations of the electric field. The variational optimization approach is based on constructing a weak form of a Lagrangian which allows to use finite element based reconstruction algorithms. The optimality conditions for the Lagrangian and stability estimate for the adjoint problem are derived, as well as Frechét differentiability of it and of the regularized Tikhonov functional are also presented. Two- and three-dimensional numerical studies confirm our theoretical investigations.

math.NA↗

arXiv2025

Reconstructing the dielectric properties of melanoma in 3D using real-life melanoma model

The paper presents performance of the adaptive domain decomposition finite element/finite difference method for reconstruction of the dielectric permittivity and conductivity functions for 3D real-life melanoma model using measurements of the backscattered electric field at the boundary of the investigated domain. We present several gradient-based reconstruction algorithms which use optimization approach to find stationary point of the Lagrangian. Our computational tests show qualitative and quantitative reconstruction of dielectric permittivity and conductivity functions using realistic model of malign melanoma at 6 GHz in 3D.

math.NA↗

arXiv2025

Finite element 3D models of melanoma growth and time-dependent backscattered data for dielectric properties of melanoma at 6 GHz

Finite element meshes for 3D models simulating realistic malignant melanoma (MM) growth, incorporating accurate dielectric properties of the skin, have been developed. Numerical simulations illustrate how 3D finite element meshes can be utilized to generate backscattered data, enabling the evaluation of reconstruction algorithms designed to determine the dielectric properties of the proposed 3D model.

math.NA↗

arXiv2025

A hybrid finite element/finite difference method for reconstruction of dielectric properties of conductive objects

The aim of this article is to present a hybrid finite element/finite difference method which is used for reconstructions of electromagnetic properties within a realistic breast phantom. This is done by studying the mentioned properties' (electric permittivity and conductivity in this case) representing coefficients in a constellation of Maxwell's equations. This information is valuable since these coefficient can reveal types of tissues within the breast, and in applications could be used to detect shapes and locations of tumours. Because of the ill-posed nature of this coefficient inverse problem, we approach it as an optimization problem by introducing the corresponding Tikhonov functional and in turn Lagrangian. These are then minimized by utilizing an interplay between finite element and finite difference methods for solutions of direct and adjoint problems, and thereafter by applying a conjugate gradient method to an adaptively refined mesh.

math.NA↗

arXiv2023

Energy norm error estimates and convergence analysis for a stabilized Maxwell's equations in conductive media

The aim of this article is to investigate the well-posedness, stability and convergence of solutions to the time-dependent Maxwell's equations for electric field in conductive media in continuous and discrete settings. The situation we consider would represent a physical problem where a subdomain is emerged in a homogeneous medium, characterized by constant dielectric permittivity and conductivity functions. It is well known that in these homogeneous regions the solution to the Maxwell's equations also solves the wave equation which makes calculations very efficient. In this way our problem can be considered as a coupling problem for which we derive stability and convergence analysis. A number of numerical examples validate theoretical convergence rates of the proposed stabilized explicit finite element scheme.

math.NA↗

arXiv2022

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

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.

math.NA↗