A single-level implementation for a fast direct method of moments solver on electrically large scattering problems using a GPU based Reduced Singular Value Decomposition block LU factorization
Bibliographic record
Abstract
In recent years there has been considerable advancement in solving large-scale electromagnetic scattering problems using fast direct solve techniques with the traditional Rao-Wilton-Glisson (RWG) Method of Moments (MoM) computational framework, and extensions to Higher Order Basis Functions (HOBF) over curvilinear elements. The direct solve techniques are typically formulated with compression algorithms such as Adaptive-Cross-Approximation (ACA/ACA+). Early attempts for PEC bodies on the CPU (J. Shaeffer, IEEE Trans. Ant. and Prop., vol. 56, no. 8, pp. 2306–2313, Aug. 2008) and dielectric composite bodies on both the CPU and GPU (M. A. Horn, T. N. Killian, and D. L. Faircloth, 2014 IEEE Ant. and Prop. Society International Symposium (APSURSI), Memphis, TN, 2014, pp. 1630–1631) implemented a Single-level (SL) block clustering scheme in which ACA/ACA+ is used for compression in both the fill and block LU factorization. More recent attempts implement Multi-level (ML) block clustering schemes utilizing hierarchical matrix (H -Matrix) theory (W. Chai and D. Jiao, 2010 IEEE Ant. and Prop. Society International Symposium (APSURSI), Toronto, ON, 2010, pp. 1–4). ML schemes rely on the compression preserving properties of the Reduced Singular Value Decomposition (rSVD) and thus do not employ ACA/ACA+ during block LU factorization.
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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 | 0.000 | 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 | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.016 | 0.006 |
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".