Parallel Fast Direct Error-Controlled Scattering Solutions via an $\mathcal{H}$-Matrix-Accelerated Locally Corrected Nyström Method for the Combined Field Integral Equation
Bibliographic record
Abstract
A parallel, fast, direct, high-order solution of the Locally Corrected Nyström (LCN) method discretization of the combined field integral equation (CFIE) is presented for solving scattering problems involving perfect electric conductors (PECs) of arbitrary shape. The discrete LCN operator is represented using the hierarchical matrix ($\mathcal{H}$-matrix) framework to accelerate the filling and solving processes, while consuming a fraction of the memory conventionally required for the dense system. The solver is validated for an exact parametrization of the surface of a sphere with quadrilateral patches (i.e., a mapped sphere). The accuracy is also studied for high-order solutions of arbitrary shapes, demonstrating a$\mathcal{O}(h^{p})$convergence. Results from this direct solver are indicative that the$\mathcal{H}$-matrix-accelerated LCN method will provide a flexible error-controllable preconditioner for general scattering problems.
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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 | 0.000 |
| 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) | 0.006 | 0.002 |
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".