Error-Controlled Static Layered-Medium Green’s Function Computation via <i>hp</i>-Adaptive Spectral Differential Equation Approximation Method
Bibliographic record
Abstract
A numerically robust and computationally efficient approach for evaluating a planar layered substrate's static Green's function is developed based on the adaptive form of the spectral differential equation approximation method. The method uses a pth-order finite element method (FEM) solution of the 1-D ordinary differential equation governing the spectrum of the layered-media Green's function with spatial h-adaptive meshing. The resulting pole-residue form of the Green's function spectrum enables analytic evaluation of the pertinent Sommerfeld integrals providing O(hp) error control of the spatial layered-medium Green's function in near, intermediate, and far zones. The detailed error analysis is presented enabling automation of the 1-D FEM mesh refinement, which guarantees a prescribed accuracy of the solution depending on the distance between the source and observation locations. The method is well suited for computing Green's function databases used by method of moments capacitance and inductance extractors.
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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 | 0.000 | 0.001 |
| 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 | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| 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".