Computed Basis Functions for Finite Element Analysis Based on Tomographic Data
Bibliographic record
Abstract
In bioelectromagnetics, the structures in which the electromagnetic field is to be computed are sometimes defined by a fine grid of voxels (3-D cells) whose tissue types are obtained by tomography. A novel finite element method is proposed for such cases. A simple, regular mesh of cube elements is constructed, each containing the same, integer number of voxels. There may be several different tissues present within an element, but this is accommodated by computing element basis functions that approximately respect the interface conditions between different tissues. Results are presented for a test model of 128 (3) voxels, consisting of nested dielectric cubes, driven by specified charges. The electrostatic potential computed with the new method agrees well with that of a conventional finite element code: the rms difference along the sample line is 1.5% of the highest voltage. Results are also presented for the potential due to a current dipole placed in a brain model of 181 × 217 × 181 voxels, derived from MRI data. The new method gives potentials that are different to those obtained by treating each voxel as an element by 1% of the peak voltage, yet the global finite element matrix has a dimension which is more than 50 times smaller.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".