Error Controllable Solutions of Large-Scale Problems in Electromagnetics: MLFMA-Accelerated Locally Corrected Nyström Solutions of CFIE in 3D [Open Problems in CEM]
Bibliographic record
Abstract
This work provides an overview of a parallel, high-order, error-controllable framework for solving large-scale scattering problems in electromagnetics, as well as open problems pertinent to such solutions. The method is based on the higher-order locally corrected Nyström (LCN) discretization of the combined-field integral equation (CFIE), accelerated with the error-controlled Multi-Level Fast Multipole Algorithm (MLFMA). Mechanisms for controlling the accuracy of calculations are discussed, including geometric representation, stages of the locally corrected Nyström method, and the MLFMA. Also presented are the key attributes of parallelization for the developed numerical framework. Numerical results validate the proposed numerical scheme by demonstrating higher-order error convergence for smooth scatterers. For the problem of scattering from a sphere, the developed numerical solution is shown to have the ability to produce a solution with a maximum relative error of the order 10-9. Open-ended problems, such as treatment of general scatterers with geometric singularities, construction of well-conditioned operators, and current challenges in development of fast iterative and direct algorithms, are also discussed.
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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 | 0.002 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".