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$k_{p}$, whereas SDEAM typically exploits a polynomial dependence on$k_{p}$. 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 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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| 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) | 0.002 | 0.001 |
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".