Matrix-Free Nodal Domain Decomposition With Relaxation For Massively Parallel Finite-Element Computation of EM Apparatus
Bibliographic record
Abstract
In this paper, the nodal domain decomposition with relaxation (NDDR) scheme is proposed to solve the nonlinear finite-element (FE) problem in electromagnetic apparatus without assembling the global system of equations. Each sub-domain contains only one node with unknown magnetic vector potential, and the calculation of each sub-domain can be massively parallelized to utilize the prevalent parallel computing architectures. The sub-domain solver has excellent modularity for single instruction multiple data programming with a specific data structure, and the required memory shows a linear increase with the problem size. The NDDR scheme is implemented on both multi-core CPUs and many-core GPUs, and the accuracy and efficiency are discussed for different problem sizes. Result comparison with a commercial FE package shows a speedup of more than 30 times for a magnetostatic case and an average speedup of more than 53 times for a time-domain nonlinear FE case with different time steps while maintaining an error of less than 0.85%.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".