A Parallel Implementation of the Correction Function Method for Poisson’s Equation With Immersed Surface Charges
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Bibliographic record
Abstract
In this paper, a novel graphics-processing unit (GPU) implementation of the recently proposed correction function method (CFM) is presented, for the finite-difference solution of Poisson problems with surface-charge distributions. The CFM is a robust and versatile method most notable for its immersed treatment of interface problems of any geometry, to an arbitrary order of accuracy. Given the well-known interface jump conditions associated with the electric scalar potential, the CFM is here shown to be immediately applicable to the computation of electrostatic fields, in the presence of curved surface-charge distributions. Moreover, an in-depth analysis of the CFM algorithm is presented, in which performance bottlenecks are investigated and significant potential for parallelizability is identified. The resulting parallel CFM algorithm is then implemented using NVIDIA's compute unified device architecture GPU language, yielding a significant increase in performance.
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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) | 0.000 | 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 it