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. AbrégéLes méthodes sans maille (MLM), comme la méthode de Galerkin sans maille (EFG), sont été proposée comme une amélioration par rapport à la méthode des éléments finis, car le besoin de génération d'une maille.Dans le domaine d'analyse électromagnétique, les MLM sont été utilisée le plus souvent dans la solution des problèmes scalaires, quasi statiques, et déterministes.Cette thèse considère une méthode EFG pour la solution des problèmes de valeur propre des guides vecteurs d'ondes : trouver les modes magnétiques transversales d'une onde en utilisant le vecteur d'onde comme la variable indéterminée.Deux méthodes sont proposées pour représenter les ondes vectrices en EFG : l'un sépare le vecteur à ses composants Cartésiens comme dans la représentation des vecteurs en éléments finis nodales, et l'autre en sépare aux deux composants.Ses composants sont un composant rotationnel et un autre irrotationnel.Ces méthodes sont essayées dans un guide d'onde avec des bords parfaitement sous courant électrique.Les solutions obtenues sont comparées du point de vue de la vérité des fréquences limites et l'élimination des modes fausses.La méthode « Cartésienne » évalue les modes actuelles correctement, mais la gamme contient des modes fausses.La deuxième méthode est un essai de l'élimination de ces modes.Les résultats indiquent que cette méthode n'élimine pas toutes les modes fausses.De plus, les modes actuelles ne sont pas exactes.
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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 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.002 |
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".