3-D Numerical Modeling for the Magnetization of Superconductors Using a Local Discontinuous Galerkin Finite Element Method
Bibliographic record
Abstract
A numerical methodology is proposed to discretize a nonlinear low-frequency approximation to Maxwell's equations using a local discontinuous Galerkin (DG) finite element method, with an upwind-like numerical flux, for modeling superconductors. In this paper, we focus on high-temperature superconductors (HTS) and the electrical resistivity is modeled using a power law. Nodal elements and the Whitney element are used. Numerical studies have been performed to verify the proposed methodology: a problem with a manufactured solution, the nonlinear magnetic front problem, and the magnetization of HTS wires. Based on the final time that can be reached for a given time-step size, the proposed strategy is compared with the H formulation discretized using the Galerkin finite element method with the Whitney element for the magnetic front problem. The proposed local DG strategy allows the use of a larger time-step size over a longer time interval, particularly, when we use the Whitney element. The proposed methodology can also capture sharp gradients of the current density with limited spurious oscillations. The numerical results are in agreement with Bean's model for large values of power-law's exponent. The proposed local DG strategy could be generalized to more complex electrical resistivity models, including multiphysics models.
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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 | 0.000 | 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 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".