A vector Element-Free Galerkin method for waveguide eigenvalue problems
Bibliographic record
Abstract
Meshless Methods such as the Element-Free Galerkin (EFG) method have been proposed as an improvement over Finite-Element Methods because they do not require a mesh.In electromagnetics, they have largely been applied to scalar, quasi-static, deterministic problems.This thesis considers an EFG method for a vector, wave, eigenvalue problem: finding the TM modes of a waveguide using the transverse magnetic field as the unknown.Two approaches are described to represent a vector field using EFG: one approach separates the field into its Cartesian components as in finite elements, and the other separates the field into a rotational and an irrotational component.The methods are tested on a rectangular waveguide with perfectly conducting walls.The solutions obtained are compared from the point of view of the accuracy of the mode cut-off frequencies and the elimination of spurious modes.It is found that the Cartesian approach evaluates the physical modes correctly, but the spectrum contains some spurious modes.The second approach is an attempt to eliminate the spurious modes.It is shown that not all of the spurious modes are removed, and moreover the physical eigenvalues are not accurate. I sincerely thank Professor Jon Webb for
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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 | 0.002 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| 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".