Sensitivity analysis for 3D Maxwell's equations and its use in the resolution of an inverse medium problem at fixed frequency

DOI10.1080/17415977.2019.1588896zbMath1486.65228arXiv1911.02409OpenAlexW3098407214MaRDI QIDQ4991464

Stéphanie Lohrengel, Jérémy Heleine, Marion Darbas

Publication date: 3 June 2021

Published in: Inverse Problems in Science and Engineering (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.02409

zbMATH Keywords

integral equationcomputer scienceGâteaux derivativeinverse medium problemedge finite elements3D Maxwell equationssmall-amplitude inhomogeneities

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory (78M10) Electromagnetic theory (general) (78A25) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Numerical methods for inverse problems for integral equations (65R32) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Optimization problems in optics and electromagnetic theory (78M50) Maxwell equations (35Q61) Numerical methods for ill-posed problems for boundary value problems involving PDEs (65N20)

Related Items (5)

Sensitivity analysis of the complete electrode model for electrical impedance tomography ⋮ A numerical algorithm based on modified orthogonal linear spline for solving a coupled nonlinear inverse reaction-diffusion problem ⋮ Current distribution reconstruction in switching arcs by means of regularization based on GSVD ⋮ Numerical resolution by the quasi-reversibility method of a data completion problem for Maxwell's equations ⋮ Asymptotic behavior of eigenvalues of the Maxwell system in the presence of small changes in the interface of an inclusion

Uses Software

• FreeFem++

Cites Work

• Unnamed Item
• Unnamed Item
• An adaptive finite element method in reconstruction of coefficients in Maxwell's equations from limited observations.
• Target identification using dictionary matching of generalized polarization tensors
• Inverse problems for the anisotropic Maxwell equations
• A new family of mixed finite elements in \({\mathbb{R}}^ 3\)
• Mathematical modeling in biomedical imaging. I: Electrical and ultrasound tomographies, anomaly detection, and brain imaging. Papers based on the minicourse, Paris, France, March 2007
• An inverse boundary value problem in electrodynamics
• Inverse acoustic and electromagnetic scattering theory.
• Identification of small amplitude perturbations in the electromagnetic parameters from partial dynamic boundary measurements.
• Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter. II: The full Maxwell equations.
• Numerical resolution of an electromagnetic inverse medium problem at fixed frequency
• EEG in neonates: forward modeling and sensitivity analysis with respect to variations of the conductivity
• Apposition of the topological sensitivity and linear sampling approaches to inverse scattering
• Reconstruction of small inhomogeneities from boundary measurements
• Inverse problems for Maxwell's equations
• Global uniqueness for an IBVP for the time-harmonic Maxwell equations
• An efficient algorithm for determining the convex hull of a finite planar set
• Numerical Reconstruction of Small Perturbations in the Electromagnetic Coefficients of a Dielectric Material
• Stable determination of the electromagnetic coefficients by boundary measurements
• Adaptive finite element method for a coefficient inverse problem for Maxwell's system
• Inclusion boundary reconstruction and sensitivity analysis in electrical impedance tomography
• Topological Sensitivity for Solving Inverse Multiple Scattering Problems in Three-dimensional Electromagnetism. Part I: One Step Method
• The Linearized Inverse Problem in Multifrequency Electrical Impedance Tomography
• Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction
• Singularities of Maxwell interface problems
• Vector potentials in three-dimensional non-smooth domains
• Mathematical foundations for error estimation in numerical solutions of integral equations in electromagnetics
• Sensitivity analysis of a nonlinear inversion method for 3D electromagnetic imaging in anisotropic media
• Topological Sensitivity for Solving Inverse Multiple Scattering Problems in Three-Dimensional Electromagnetism. Part II: Iterative Method
• Finite Element Methods for Maxwell's Equations
• Electrical impedance tomography
• New development in freefem++
• Resolution-Controlled Conductivity Discretization in Electrical Impedance Tomography
• Numerical determination of anomalies in multifrequency electrical impedance tomography
• The generalized polarization tensors for resolved imaging Part II: Shape and electromagnetic parameters reconstruction of an electromagnetic inclusion from multistatic measurements
• Acoustic and electromagnetic equations. Integral representations for harmonic problems

This page was built for publication: Sensitivity analysis for 3D Maxwell's equations and its use in the resolution of an inverse medium problem at fixed frequency