Fast Direct Method of Moments Solution of Surface-Volume-Surface Integral Equation with H-Matrices
Bibliographic record
Abstract
The Surface-Volume-Surface Electric Field Integral Equation (SVS-EFIE) [1] is a single-source integral equation which can be formulated for solution of radiation and scattering problems on homogeneous as well as piece-wise homogeneous (composite) penetrable objects. The Method of Moments (MoM) discretization of SVS-EFIE produces three dense matrices corresponding to its three integral operators. These operators map the field from the scatterer's surface to its volume, from its volume to its surface, and from its surface to back its surface. Because of the discretization of both the surface and the volume of the scatterer the resultant dense matrices take large amount of memory and require prolonged computational time, if handled directly. In this work we demonstrate a computational framework based on the theory of hierarchical matrices (H-matrices) [2], which allows to greatly alleviate the CPU time and memory complexity of the SVS-EFIE MoM solution.
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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) | 0.000 | 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) | 0.005 | 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".