Reconstruction of capacitance tomography images of simulated two-phase flow regimes

Gómez, Susana; Ono, M.; Gamio, Carlos; Fraguela, A.

doi:10.1016/s0168-9274(02)00253-2

Cited by 16 publications

(10 citation statements)

References 6 publications

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“…This gives us 54 results (2 problems × 9 values of k × 3 initial points) for the estimations 1 k and 2 k , k = 1, , 9 In several Note that index j is associated with the 3 initial points for the optimization method. A total of 108 problems have been solved and, in the following Appendix, comparisons of these magnitudes are shown with 3 graphs of performance profiles.…”

Section: Numerical Resultsmentioning

confidence: 99%

See 1 more Smart Citation

A Globally Convergent Algorithm for a PDE-Constrained Optimization Problem Arising in Electrical Impedance Tomography

Carrillo

Gómez

2015

Numerical Functional Analysis and Optimization

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We study the convergence properties of an algorithm for the inverse problem of electrical impedance tomography, which can be reduced to a partial differential equation (PDE) constrained optimization problem. The direct problem consists of the potential equation div( u) = 0 in a circle, with Neumann condition describing the behavior of the electrostatic potential in a medium with conductivity given by the function (x, y). We suppose that at each time a current i is applied to the boundary of the circle (Neumann's data), and that it is possible to measure the corresponding potential i (Dirichlet data). The inverse problem is to find (x, y) given a finite number of Cauchy pairs measurements ( i , i ), i = 1, , N . The problem is formulated as a least squares problem, and the developed algorithm solves the continuous problem using descent iterations in its corresponding finite element approximations. Wolfe's conditions are used to ensure the global convergence of the optimization algorithm for the continuous problem. Although exact data are assumed, measurement errors in data and regularization methods shall be considered in a future work.

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Section: Numerical Resultsmentioning

confidence: 99%

“…for both, the continuous (7)-(8)- (9) and discrete (18)-(19)- (20) problems, by Lemma 1 and convexity, we deduce from the necessary optimality conditions of discrete problems:…”

Section: Convergence Of Gradientsmentioning

confidence: 93%

A Globally Convergent Algorithm for a PDE-Constrained Optimization Problem Arising in Electrical Impedance Tomography

Carrillo

Gómez

2015

Numerical Functional Analysis and Optimization

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“…errors between b T k À T e and T k À T e (7). As the errors are characteristic of the equipment, there is the unusual fact that the error in the approximation of function H by this methodology is independent of the function.…”

Section: Remarkmentioning

confidence: 99%

“…These functions and parameters are determined usually either by experimentation based protocols [3] or by solving inverse problems posed in an appropriate mathematical framework (see, e.g. [5][6][7]). Other works regarding numerical approaches for inverse problems can be seen in [8,9].…”

Section: Introductionmentioning

confidence: 99%

Identification of a heat transfer coefficient depending on pressure and temperature

Fraguela

Río

Ramos

et al. 2011

Inverse Problems in Science and Engineering

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This article deals with an inverse problem concerning the identification of the heat exchange coefficient H (assumed depending on the temperature and/or pressure) between a certain material with the external environment, when only experimental measurements of the temperature are supposed to be known. The main difficulties are that we consider the case of functions H depending on the solution of the state equation and we use experimental data that may have errors. We develop rigorous mathematical strategies for this identification. We separately consider pressure and temperature dependence and, in both cases, we set several scenarios for the inverse problem. For each scenario, we know the initial and ambient temperatures, we identify function H through different methods and we obtain error bounds in adequate norms (uniform and square integrable). Finally, we perform numerical tests in order to compare the results obtained with these algorithms and with some classical regularization algorithms.

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“…We take E = -∇u and in the absence of internal charges: where ε is dielectric permittivity, χ k is the k-th electrode, held at the potential Vk which is non-zero for an excitation electrode and zero for sensing electrodes [5] .…”

Section: The Forward Problem In Ectmentioning

confidence: 99%

Three-dimensional electrical capacitance tomography imaging

Soleimani¹

2006

Insight - Non-Destructive Testing and Condition Monitoring

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Reconstruction of capacitance tomography images of simulated two-phase flow regimes

Cited by 16 publications

References 6 publications

A Globally Convergent Algorithm for a PDE-Constrained Optimization Problem Arising in Electrical Impedance Tomography

A Globally Convergent Algorithm for a PDE-Constrained Optimization Problem Arising in Electrical Impedance Tomography

Identification of a heat transfer coefficient depending on pressure and temperature

Three-dimensional electrical capacitance tomography imaging

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