Closed-Form Evaluation of Mixed Potential Shielded Layered Media Green’s Functions With Spectral Differential Equation Approximation Method
Bibliographic record
Abstract
A novel, robust, and computationally efficient approach is proposed for the evaluation of the Michalski–Zheng’s mixed-potential Green’s functions of general shielded layered media. A high-order variant of the spectral differential equation approximation method (SDEAM) is used to cast the spectra of Green’s functions’ components into pole-residue forms. The latter allows for closed-form evaluation of the Sommerfeld integrals (SIs) defining spatial components of the mixed-potential Green’s functions required by Method-of-Moment (MoM) discretization of different types of integral equations. The method produces Green’s functions for all elevations of interest at a fixed cost, making it substantially faster than popular alternative approaches. Numerical results validate the developed high-order SDEAM scheme and demonstrate its extended range of validity compared to the discrete complex image method (DCIM).
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| 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) | 0.001 | 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 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".