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 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 | 0.002 | 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 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".