A General Space-filling Curve Algorithm for Partitioning 2D Meshes
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Bibliographic record
Abstract
This paper describes a recursive algorithm for constructing a general Space-Filling Curve (SFC) for an arbitrary distribution of points in 2D. We use the SFC to partition 2D meshes, both structured and unstructured, and compare the quality of partitions with traditional SFCs and the multilevel partitioning schemes of Metis and Scotch. The algorithm is independent of the geometry of the mesh and can be easily adapted to irregular meshes. We discuss the advantages of SFCs over multilevel partitioners for meshes in scientific simulations. We define three performance metrics for a reasonable comparison of partitions: volume or load per partition, degree or the number of distinct edges of a partition in the communication graph and communication volume or the sum of the weights of outgoing edges for each partition in the communication graph. We propose a performance model for modern architectures using these metrics. We find our partitions comparable to and in some cases better than the best multilevel partitions, while being computed much faster. Unlike Metis, our hierarchical approach yields good hierarchical partitions (e.g., for partitioning to node and core level), and is appropriate for adaptive mesh refinement kernels.
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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