Convolutional CFS-PML for the 2-D Crank–Nicolson FDTD Scheme and Its Application in Simulation of Ultralow Frequency Electromagnetic Problems
Bibliographic record
Abstract
A convolutional implementation of the perfectly matched layer (PML) absorbing boundary condition (ABC) with complex frequency-shifted (CFS) constitutive parameters is developed for the original 2-D Crank-Nicolson (CN) scheme of the finite-difference time-domain (FDTD) method. The proposed CN-FDTD method leverages the benefits of both CFS-PML and the unconditionally stable CN scheme, overcoming the stability limits of the conventional FDTD method and decreasing the numerical reflection of evanescent waves. The effectiveness of the proposed scheme is validated by conducting an analysis of the absorbing boundary reflection error and the simulation speed. For an ultralow frequency and small-scale problem with an extremely fine spatial mesh size ($2\times 10^{7}$times smaller than the minimum exited wavelength) and using time steps$4\times 10^{6}$times larger than those in conventional FDTD, we achieved a CPU time improvement of up to$2.9360\times 10^{4}$times compared to the conventional FDTD method, with less than 3% numerical error.
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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 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".