Parallel Fast Direct Error-Controlled Scattering Solutions via an $\mathcal{H}$-Matrix-Accelerated Locally Corrected Nyström Method for the Combined Field Integral Equation
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
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 (<tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{H}$</tex>-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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{O}(h^{p})$</tex> convergence. Results from this direct solver are indicative that the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{H}$</tex>-matrix-accelerated LCN method will provide a flexible error-controllable preconditioner for general scattering problems.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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) | 0.001 | 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 it