Related papers: A hybrid finite element/finite difference method f…
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…
We propose an adaptive finite element method for the solution of a coefficient inverse problem of simultaneous reconstruction of the dielectric permittivity and magnetic permeability functions in the Maxwell's system using limited boundary…
We consider a coefficient inverse problem for the dielectric permittivity in Maxwell's equations, with data consisting of boundary measurements of one or two backscattered or transmitted waves. The problem is treated using a Lagrangian…
In this work we develop and analyze an adaptive finite element method for efficiently solving electrical impedance tomography -- a severely ill-posed nonlinear inverse problem for recovering the conductivity from boundary voltage…
We consider the inverse problem of the simultaneous reconstruction of the dielectric permittivity and magnetic permeability functions of the Maxwell's system in 3D with limited boundary observations of the electric field. The theoretical…
We present domain decomposition finite element/finite difference method for the solution of hyperbolic equation. The domain decomposition is performed such that finite elements and finite differences are used in different subdomains of the…
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…
We present the Finite Element Method (FEM) for the numerical solution of the multidimensional coefficient inverse problem (MCIP) in two dimensions. This method is used for explicit reconstruction of the coefficient in the hyperbolic…
We present a posteriori error estimates for finite element approximations in a minimization approach to a coefficient inverse problem. The problem is that of reconstructing the dielectric permittivity $\varepsilon =…
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…
Magnetic resonance electrical property tomography is a recent medical imaging modality for visualizing the electrical tissue properties of the human body using radio-frequency magnetic fields. It uses the fact that in magnetic resonance…
We study the shape reconstruction of an inclusion from the {faraway} measurement of the associated electric field. This is an inverse problem of practical importance in biomedical imaging and is known to be notoriously ill-posed. By…
Calculations of the photonic band structure, transmission coefficients, and quality factors of various two-dimensional, periodic and aperiodic, dielectric photonic crystals by using the finite element method (FEM) are reported. The…
Fluorescence molecular tomography (FMT) has potential of providing high contrast images for breast tumor detection. Computational phantom provides a convenient way to a wide variety of fluorophore distribution configurations in patients and…
In the analysis of composite materials with heterogeneous microstructures, full resolution of the heterogeneities using classical numerical approaches can be computationally prohibitive. This paper presents a micromechanics-enhanced finite…
Maxwell's equations describe the evolution of electromagnetic fields, together with constraints on the divergence of the magnetic and electric flux densities. These constraints correspond to fundamental physical laws: the nonexistence of…
This paper develops an enhanced finite element method for approximating a class of variational problems which exhibit the \textit{Lavrentiev gap phenomenon} in the sense that the minimum values of the energy functional have a nontrivial gap…
We develop a cut finite element method (CutFEM) for convection-diffusion problems posed on mixed-dimensional domains, i.e., unions of manifolds of different dimensions arranged in a hierarchical structure where lower-dimensional components…
The convergence of an adaptive mixed finite element method for general second order linear elliptic problems defined on simply connected bounded polygonal domains is analyzed in this paper. The main difficulties in the analysis are posed by…
We present useful connections between the finite difference and the finite element methods for a model boundary value problem. We start from the observation that, in the finite element context, the interpolant of the solution in one…