A Systematic Approach to Adaptive Mesh Refinement for Computational Electrodynamics
Bibliographic record
Abstract
There is a great need to solve CED problems on adaptive meshes; referred to here as AMR-CED. The problem was deemed to be susceptible to “long-term instability” and parameterized methods have been used to control the instability. In this paper, we present a new class of AMR-CED methods that are free of this instability because they are based on a more careful understanding of the constraints in Maxwell's equations and their preservation on a single control volume. The important building blocks of these new methods are: 1) Timestep sub-cycling of finer child meshes relative to parent meshes. 2) Restriction of fine mesh facial data to coarser meshes when the two meshes are synchronized in time. 3) Divergence constraint-preserving prolongation of the coarse mesh solution to newly built fine meshes or to the ghost zones of pre-existing fine meshes. 4) Electric and magnetic field intensity-correction strategy at fine-coarse interfaces. Using examples, we show that the resulting AMR-CED algorithm is free of “long-term instability”. Unlike previous methods, there are no adjustable parameters. The method is inherently stable because a strict algorithmic consistency is applied at all levels in the AMR mesh hierarchy. We also show that the method preserves order of accuracy, so that high order methods for AMR-CED are indeed 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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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".