Impact of particle number and cell size in fully implicit charge- and energy-conserving particle-in-cell schemes
Bibliographic record
Abstract
Fully implicit charge- and energy-conserving electrostatic particle-in-cell codes have recently been investigated for their potential to model plasmas at temporal and spatial scales larger than the plasma period and Debye length, respectively. Recent literature on the topic emphasizes the accuracy of these codes, and more importantly for many researchers, the prospect of orders of magnitude speedup of plasma simulations in 3D (three dimensions). In this paper, we further examine previous case studies on 1D fully implicit charge- and energy-conserving electrostatic codes by varying numerical parameters to determine whether this scalability is achievable. We first apply the scheme on an ion acoustic shockwave with periodic conditions, and then to a series of benchmarks for bounded capacitively coupled radio-frequency plasmas. Our findings show that to reproduce highly resolved convergent solutions, a higher amount of particles per cell need to be used in the implicit scheme for both periodic and bounded simulations when the cell size exceeds the Debye length. The addition of non-uniform grids and collisions is found to exacerbate the errors in the final solutions for the bounded plasma case using the implicit scheme. Combined with the higher computational cost of particle calculations vs field solvers, we found that the implicit scheme leads to an increased runtime in 1D (one dimension) compared to the explicit momentum-conserving algorithm when accuracy relative to a well-resolved converged solution is required.
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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 | 0.002 | 0.014 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".