Finite formulation with an incentric dual mesh for time-harmonic electromagnetics
Bibliographic record
Abstract
A Finite Formulation technique, the Cell Method, is developed in the framework of an incentric dual mesh and applied to the general problem of guided wave structures.cell Method is a numerical technique which uses a primal-dual mesh complex and global (integral) variables instead of field variables (densities).In the Cell Method, Maxwell,s curl equations are exactly discretized as topological relations.Constitutive relations, on the other hand, are approximately discretized by the use of a proper dual mesh.The common choice for construction of the dual mesh is the barycentric scheme which produces non-diagonal constitutive matrices.A new time-harmonic finite formulation using a non-orthogonal dual mesh is presented which is based on choosing incenters of primal triangles as an altemative to barycentric dual points.In the incentric fonnulation, diagonal constitutive matrices are obtained which result in a syrnmetric positive definite eigenvalue problem in the first step (zero-order approxirnation).A minimization procedure is then utilized to take into account the non-orthogonality of the dual mesh and efficiently improve the accuracy of the zero-ord.ersolution.An eigenvalue system with symmetric positive definite constitutive matrices assures the stability and convergence of the solution while being computationally inexpensive.In this thesis, the finite formulation for time-harmonic electromagnetic is described in detail' This is followed by a comprehensive theoretical explanation about the proposed incentric scheme.Several examples of electromagnetic problems including multi-scale geometries and inhomogeneous media are presented.Results of applying the proposed numerical technique are compared with the results obtained from a Finite Element Method' Analytical solutions are also used for comparison wherever possible.
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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 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".