$\mathcal {H}$-Matrix Accelerated Solution of Surface–Volume–Surface EFIE for Fast Electromagnetic Analysis on 3-D Composite Dielectric Objects
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Bibliographic record
Abstract
An efficient fast direct algorithm based on the hierarchical ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}$</tex-math></inline-formula> -) matrices is presented for solution of the radiation problems on piecewise homogeneous dielectric objects using Method of Moment (MoM) discretization of the surface–volume–surface electric field integral equation (SVS-EFIE). The SVS-EFIE for the composite objects introduces independent surface electric current density on the boundary of each region. Therefore, different from the traditional Poggio–Miller–Chang–Harrington–Wu–Tsai formulation, in the SVS-EFIE, the object regions can be meshing independently according to their local properties which improves the flexibility and efficiency of the proposed method. It also makes the proposed algorithms appropriate for the analysis of both multiscale and large-scale composite structures. The numerical results from the proposed fast method are provided for the high-loss biological tissues from bioelectromagnetics applications and agree well with the analytical Mie series solution and commercial software. The CPU time and memory cost of the required <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}$</tex-math></inline-formula> -matrix operations are analyzed in details and verified through several numerical experiments. The new computational framework allows for fast direct solution of 3-D radiation and scattering problems of moderate electrical size with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$O(P^{\alpha } \log ^2 P)$</tex-math></inline-formula> CPU time and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$O(P^{\alpha } \log P)$</tex-math></inline-formula> memory complexity, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$P$</tex-math></inline-formula> being the number of surface unknowns produced by the MoM discretization, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1\leq \alpha \leq 1.5$</tex-math></inline-formula> being a geometry-dependent parameter.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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) | 0.000 | 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 it