On the Efficient Evaluation of the Azimuthal Fourier Components of the Green's Function for Helmholtz's Equation in Cylindrical Coordinates
Bibliographic record
Abstract
In this manuscript, we develop an efficient algorithm to evaluate the azimuthal Fourier components of the Green's function for the Helmholtz equation in cylindrical coordinates. A computationally efficient algorithm for this modal Green's function is essential for solvers for electromagnetic scattering from bodies of revolution (e.g., radar cross sections, antennas). Current algorithms to evaluate this modal Green's function become computationally intractable when the source and target are close or when the wavenumber is large. Furthermore, most state of the art methods cannot be easily parallelized. In this manuscript, we present an algorithm for evaluating the modal Green's function that has performance independent of both source-to-target proximity and wavenumber, and whose cost grows as $O(m)$, where $m$ is the Fourier mode. Furthermore, our algorithm is embarrassingly parallelizable.
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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) | 0.000 | 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".