2-D Thin-Shell Model Based on the $H$-$\phi$-Formulation for Modeling HTS Tapes in COMSOL Multiphysics
Bibliographic record
Abstract
This article presents a finite-element thin-shell (TS) model and its application to 2-D electromagnetic problems involving superconducting tapes in COMSOL Multiphysics. The magnetic scalar potential ($\phi$) is the state variable in nonconducting regions surrounding of the tapes, which are represented as zero thickness objects in the calculus domain. Inside the tapes, an auxiliary 1-D problem formulated in terms of the tangential components of the magnetic field ($H$) takes into account the physics across their thickness. The final finite-element system of equations includes both the 2-D and 1-D discretized equations, which are solved simultaneously in a fully coupled manner and transparently for the user. The use of thin cuts is required to impose transport currents in the tapes. This procedure allows the simulation of problems comprising superconducting tapes in any geometrical configuration. We demonstrate that both the normal and tangential fields agree well with reference solutions obtained with the widely used$T$-$A$-formulation and with the more standard$H$- and$H$-$\phi$-formulations with a full 2-D discretization of the tapes. The proposed$H$-$\phi$TS model estimates ac losses accurately while speeding up simulations. This makes this model ideal for simulating large-scale superconducting devices in 2-D, particularly when they comprise compact arrangements of high-temperature superconductor tapes carrying antiparallel currents.
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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) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| 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".