RECORD
Adaptive Reconstruction for Electrical Impedance Tomography with a Piecewise Constant Conductivity
Numerical Analysis · Submitted 18 Apr 2019
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We prove the convergence of the adaptive algorithm in the following sense: the sequence of discrete solutions contains a subsequence convergent to a solution of the continuous necessary optimality system.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
In this work we propose and analyze a numerical method for electrical impedance tomography of recovering a piecewise constant conductivity from boundary voltage measurements. It is based on standard Tikhonov regularization with a Modica-Mortola penalty functional and adaptive mesh refinement using suitable a posteriori error estimators of residual type that involve the state, adjoint and variational inequality in the necessary optimality condition and a separate marking strategy. We prove the convergence of the adaptive algorithm in the following sense: the sequence of discrete solutions contains a subsequence convergent to a solution of the continuous necessary optimality system. Several numerical examples are presented to illustrate the convergence behavior of the algorithm.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In this work we propose and analyze a numerical method for electrical impedance tomography of recovering a piecewise constant conductivity from boundary voltage measurements. | contribution 1.00 | 0.88 | 0.08 | asserted 0.99 |
| s1 | It is based on standard Tikhonov regularization with a Modica-Mortola penalty functional and adaptive mesh refinement using suitable a posteriori error estimators of residual type that involve the state, adjoint and variational inequality in the necessary optimality condition and a separate marking strategy. | method 0.99 | 0.82 | 0.05 | asserted 1.00 |
| s2 | We prove the convergence of the adaptive algorithm in the following sense: the sequence of discrete solutions contains a subsequence convergent to a solution of the continuous necessary optimality system. | result 0.89 | 0.95 | 0.66 | asserted 1.00 |
| s3 | Several numerical examples are presented to illustrate the convergence behavior of the algorithm. | contribution 0.43 | 0.93 | 0.06 | asserted 0.99 |
What was examined, and what was not
- arXiv listing abstract v1
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
In this work we propose and analyze a numerical method for electrical impedance tomography of recovering a piecewise constant conductivity from boundary voltage measurements. It is based on standard Tikhonov regularization with a Modica-Mortola penalty functional and adaptive mesh refinement using suitable a posteriori error estimators of residual type that involve the state, adjoint and variational inequality in the necessary optimality condition and a separate marking strategy. We prove the convergence of the adaptive algorithm in the following sense: the sequence of discrete solutions contains a subsequence convergent to a solution of the continuous necessary optimality system. Several numerical examples are presented to illustrate the convergence behavior of the algorithm.
Human review
How the literature uses it
What this paper does with the arXiv papers it cites
What it cites
Uses the method or tool of 1 paper
-
Then one linearized approximation $p_L(z,z_k)$ reads (with $δz=z-z_k$) [equation] Upon substituting the approximation $p_L(z,z_k)$ for $p(z)$ and linearizing the forward map $U(σ)$, we obtain the following surrogate energy functional (with $δσ=σ-σ_k$ being the increment and $δU= U^δ-U(σ_k)$) [equation] The treatment of the double well potential term $∫_ΩW(σ)dx$ is in the spirit of the classical majorization-minimization algorithm in the following sense (see [ref] for a detailed derivation) [equation] This algorithm is known to have excellent numerical stability.
A Minimization Method for The Double-Well Energy Functional · The solution of the variational inequality · 0.93
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.