Parallel Adaptive Mesh Refinement Combined with Additive Multigrid for the Efficient Solution of the Poisson Equation
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Bibliographic record
Abstract
Three different speed-up methods (viz., additive multigrid method, adaptive mesh refinement (AMR), and parallelization) have been combined in order to provide a highly efficient parallel solver for the Poisson equation. Rather than using an ordinary tree data structure to organize the information on the adaptive Cartesian mesh, a modified form of the fully threaded tree (FTT) data structure is used. The Hilbert space-filling curve (SFC) approach has been adopted for dynamic grid partitioning (resulting in a partitioning that is near optimal with respect to load balancing on a parallel computational platform). Finally, an additive multigrid method (BPX preconditioner), which itself is parallelizable to a certain extent, has been used to solve the linear equation system arising from the discretization. Our numerical experiments show that the proposed parallel AMR algorithm based on the FTT data structure, Hilbert SFC for grid partitioning, and additive multigrid method is highly efficient.
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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