A PPPM fast summation method for fluids and beyond
Why this work is in the frame
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Bibliographic record
Abstract
Solving the N -body problem, i.e. the Poisson problem with point sources, is a common task in graphics and simulation. The naive direct summation of the kernel function over all particles scales quadratically, rendering it too slow for large problems, while the optimal Fast Multipole Method has drastic implementation complexity and can sometimes carry too high an overhead to be practical. We present a new Particle-Particle Particle-Mesh (PPPM) algorithm which is fast, accurate, and easy to implement even in parallel on a GPU. We capture long-range interactions with a fast multigrid solver on a background grid with a novel boundary condition, while short-range interactions are calculated directly with a new error compensation to avoid error from the background grid. We demonstrate the power of PPPM with a new vortex particle smoke solver, which features a vortex segment-approach to the stretching term, potential flow to enforce no-stick solid boundaries on arbitrary moving solid boundaries, and a new mechanism for vortex shedding from boundary layers. Comparison against a simpler Vortex-in-Cell approach shows PPPM can produce significantly more detailed results with less computation. In addition, we use our PPPM solver for a Poisson surface reconstruction problem to show its potential as a general-purpose Poisson solver.
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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