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Reconstruction of dielectrics from experimental data via a hybrid globally convergent/adaptive inverse algorithm, Inverse Problems, accepted for publication
, 2010
"... The validity of a synthesis of a globally convergent numerical method with the adaptive FEM technique for a coefficient inverse problem is verified on time resolved experimental data. Refractive indices, locations and shapes of dielectric abnormalities are accurately imaged. 1 ..."
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Cited by 15 (6 self)
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The validity of a synthesis of a globally convergent numerical method with the adaptive FEM technique for a coefficient inverse problem is verified on time resolved experimental data. Refractive indices, locations and shapes of dielectric abnormalities are accurately imaged. 1
Parallel Algorithms for PDEConstrained Optimization and Application to Optimal Control of Viscous Flows
, 2000
"... PDEconstrained optimization refers to the optimization of systems governed by partial differential equations (PDEs). The simulation problem is to solve the PDEs for the state variables (e.g. displacement, velocity, temperature, electric field, magnetic field, species concentration), given appropria ..."
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Cited by 4 (1 self)
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PDEconstrained optimization refers to the optimization of systems governed by partial differential equations (PDEs). The simulation problem is to solve the PDEs for the state variables (e.g. displacement, velocity, temperature, electric field, magnetic field, species concentration), given appropriate data (e.g. geometry, coefficients, boundary conditions,
1 BLIND BACKSCATTERING EXPERIMENTAL DATA COLLECTED IN THE FIELD AND AN APPROXIMATELY GLOBALLY CONVERGENT INVERSE ALGORITHM
"... An approximately globally convergent numerical method for a 1D Coefficient Inverse Problem for a hyperbolic PDE is applied to image dielectric constants of targets from blind experimental data. The data were collected in the field by the Forward Looking Radar of the US Army Research Laboratory. A p ..."
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Cited by 3 (1 self)
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An approximately globally convergent numerical method for a 1D Coefficient Inverse Problem for a hyperbolic PDE is applied to image dielectric constants of targets from blind experimental data. The data were collected in the field by the Forward Looking Radar of the US Army Research Laboratory. A posteriori analysis has revealed that computed and tabulated values of dielectric constants are in a good agreement. Convergence analysis is presented.
A GLOBALLY CONVERGENT NUMERICAL METHOD FOR SOME COEFFICIENT INVERSE PROBLEMS WITH RESULTING SECOND ORDER ELLIPTIC EQUATIONS
"... Abstract. A new globally convergent numerical method is developed for some multidimensional Coefficient Inverse Problems for hyperbolic and parabolic PDEs with applications in acoustics, electromagnetics and optical medical imaging. On each iterative step the Dirichlet boundary value problem for a s ..."
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Abstract. A new globally convergent numerical method is developed for some multidimensional Coefficient Inverse Problems for hyperbolic and parabolic PDEs with applications in acoustics, electromagnetics and optical medical imaging. On each iterative step the Dirichlet boundary value problem for a second order elliptic equation is solved. The global convergence is rigorously proven and numerical experiments are presented. 1.
Coefficient Inverse Problems for Imaging Inhomogeneities
"... How can we differentiate between an underground stone and a land mine? We discuss a class of methods for solving such problems. This class of methods concerns globally convergent numerical methods for Coefficient Inverse Problems, unlike conventional locally convergent algorithms. Numerical results ..."
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How can we differentiate between an underground stone and a land mine? We discuss a class of methods for solving such problems. This class of methods concerns globally convergent numerical methods for Coefficient Inverse Problems, unlike conventional locally convergent algorithms. Numerical results are presented modeling imaging of the spatially distributed dielectric permittivity function in an environment where antipersonnel land mines are embedded along with stones. While these results are concerned with the first generation of globally convergent algorithms, images obtained by the most recent second generation are also presented for a generic case of imaging of the dielectric permittivity function. The mathematical apparatus is sketched only very briefly with references to corresponding publications. 1
A posteriori error estimates for the adaptivity technique for the Tikhonov functional and global convergence for a coefficient inverse problem
, 2009
"... A synthesis of a globally convergent numerical method for a coefficient inverse problem and the adaptivity technique is presented.
First, the globally convergent method provides a good approximation for the unknown coefficient. Next, this approximation is refined via the adaptivity technique.
The ..."
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A synthesis of a globally convergent numerical method for a coefficient inverse problem and the adaptivity technique is presented.
First, the globally convergent method provides a good approximation for the unknown coefficient. Next, this approximation is refined via the adaptivity technique.
The analytical effort is focused on a posteriori error estimates for the adaptivity.
A numerical test is presented.
A globally convergent numerical method and adaptivity for a hyperbolic coefficient inverse problem
, 2009
"... A globally convergent numerical method for a multidimensional Coefficient Inverse Problem for a hyperbolic equation is presented.
It is shown that this technique provides a good starting point for the socalled finite element adaptive method (adaptivity).
This leads to a natural twostage numerica ..."
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A globally convergent numerical method for a multidimensional Coefficient Inverse Problem for a hyperbolic equation is presented.
It is shown that this technique provides a good starting point for the socalled finite element adaptive method (adaptivity).
This leads to a natural twostage numerical procedure, which synthesizes both these methods.
Numerical examples are presented.
INVERSE PROBLEMS
, 2007
"... doi:10.1088/02665611/23/3/018 Effect of discretization error and adaptive mesh generation in diffuse optical absorption imaging: II ..."
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doi:10.1088/02665611/23/3/018 Effect of discretization error and adaptive mesh generation in diffuse optical absorption imaging: II
Elastic electron scattering using the Finite Element Method: forward and inverse problems
, 2012
"... ABSTRACT. We address here the case of electronmatter elastic interaction as it occurs in Transmission Electron Microscopy (TEM) experiments. In the forward problem, we show that it is possible to derive the scattered electron wave function as the solution of a Helmholtz equation. This equation depe ..."
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ABSTRACT. We address here the case of electronmatter elastic interaction as it occurs in Transmission Electron Microscopy (TEM) experiments. In the forward problem, we show that it is possible to derive the scattered electron wave function as the solution of a Helmholtz equation. This equation depends on the spatial potential associated with the analyzed sample, and can be relevantly solved using the Finite Element Method (FEM). Then we present an inverse formulation dealing with the determination of the sample’s potential when the total wave function is measured after crossing the sample. RÉSUMÉ. Nous nous intéressons ici au cas de l’interaction élastique électronmatière rencontrée dans un microscope électronique en transmission (MET). À partir du potentiel spatial caractérisant l’échantillon observé, nous montrons que le problème direct permettant d’obtenir la fonction d’onde électronique à la sortie de l’échantillon peut s’écrire comme une équation de Helmholtz, qui peut être résolue de façon pertinente par la Méthode des Éléments Finis (MEF). Une formulation du problème inverse qui a pour but de retrouver le potentiel de l’échantillon à partir de la fonction d’onde mesurée est également présentée.