Closed-Form Evaluation of Michalski-Zheng's Mixed Potential Green's Function in Unbounded Layered Media Using High-Order DGM-Based SDEAM
Bibliographic record
Abstract
The Spectral Differential Equation Approximation Method (SDEAM) provides a closed-form approximation of the Sommerfeld integral and serves as an attractive alternative to existing Green's function approximation techniques. Recently, a high-order Discontinuous-Galerkin-Method (DGM) implementation of SDEAM for the Michalski-Zheng's mixed potential Green's function in shielded layered medium has been developed. For unbounded layered media, the radiation boundary condition (RBC) introduces an irrational dependence on the spectral lateral distance <tex>$k_{p}$</tex>, whereas SDEAM typically exploits a polynomial dependence on <tex>$k_{p}$</tex>. This issue can be addressed by fitting this irrational dependence with rational functions. In this work, the high-order DGM-based SDEAM is augmented with the rational function fitting method in an effort to achieve an error-controllable framework for evaluating the mixed potential Green's function for RBCs. Consideration is limited to those Green's function components needed to solve 2.5D problems.
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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 | 0.001 |
| 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) | 0.004 | 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".