Finite Element Approximation and Numerical Analysis of Three-dimensional Electrical Impedance Tomography
Bibliographic record
Abstract
Electrical impedance tomography is solved by solving an inverse problem of elliptic equation, and a new numerical method or a new technique is argued to consider finite element (such as normal element and mixed element) in this paper on three dimensional region. Introducing different perturbations to boundary restrictions and using different spacial steps, the authors obtain numerical solutions and give comparison with exact solutions. Numerical data show that numerical solution can approximate exact solution well as spacial step taken small and the approximation of Neumann boundary condition is more stable than that of Dirichlet case. For Newton iterations on finite element method, a large-scaled system of massive linear equations is solved in each iteration, thus the computation is quite expensive. So two techniques are argued in the first half of this paper. Firstly, the invariance property of quasi-element stiffness matrix is used in the iterations and a type of special current model is introduced. Then the minimum number of direct problems solved is considered. Later a local conservative numerical approximation, low order mixed element (block-centered method) is presented in the latter part and the positive semi-definiteness and the existence of its solution are proved. Computational formula of error functional Jacobi matrix is derived and the least direct problems in each iteration are solved by using the symmetry of algorithm and a special current basis. This method has been applied successfully in actual numerical simulation of three-dimensional electrical impedance tomography.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".