COMSOL Implementation of the H-$\phi$-Formulation With Thin Cuts for Modeling Superconductors With Transport Currents
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Bibliographic record
Abstract
Despite the acclaimed success of the magnetic field (H) formulation for modeling the electromagnetic behavior of superconductors with the finite-element method, the use of vector-dependent variables in nonconducting domains leads to unnecessarily long computation times. In order to solve this issue, we have recently shown how to use a magnetic scalar potential together with the H-formulation in the COMSOL Multiphysics environment to efficiently and accurately solve for the magnetic field surrounding superconducting domains. However, from the definition of the magnetic scalar potential, the nonconducting domains must be made simply connected in order to obey Ampere's law. In this article, we use thin cuts to apply a discontinuity in Φ and make the nonconducting domains simply connected. This approach is shown to be easily implementable in the COMSOL Multiphysics finite-element program, already widely used by the applied superconductivity community. We simulate three different models in two dimensions and three dimensions using superconducting filaments and tapes, and show that the results are in very good agreement with the H-A and H-formulations. Finally, we compare the computation times between the formulations, showing that the H-Φ-formulation can be up to seven times faster than the standard H-formulation in certain applications of interest.
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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 | 0.000 | 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 | 0.002 |
| 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)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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