Novel single-source integral equation for accurate quasi-magneto-static modeling of current flow in 3D conductors
Bibliographic record
Abstract
Summary form only given. Accurate modeling of current flow in 3D conductors has important applications in signal integrity analysis of high-speed interconnects, time-domain analysis of power delivery in transmission lines, and various other areas. In our recent work (Menshov, IEEE T-MTT, Dec. 2012) we proposed a new rigorous single source integral equation for magnetostatic analysis of 2D transmission lines and full-wave TM scattering on cylinders of arbitrary cross-sections. The new integral equation is derived from the classical Volume Electric Field Integral Equation (V-EFIE) through representation of the internal field in the object in the form of the single-layer ansatz. This converts the V-EFIE into the form of a surface integral equation featuring only a single unknown function on the surface of the object. It also features a product of surface and volume operators, terming new equation the Surface-Volume-Surface EFIE (SVS-EFIE). The SVS-EFIE equation was shown to be rigorous in nature and produce error controllable solution of the magnetostatic and full-wave problems in 2D. In this work we generalize the SVS-EFIE formulation to 3D for the magneto-quasi-static analysis of current flow in conductors of arbitrary cross-sections. Such analysis has been foundational to the inductance extraction problems (Kamon, et.al., IEEE T-MTT, Sept. 1994) in VLSI interconnects, bond-wires, and other types of transmission lines. Due to its rigorous nature the proposed new 3D SVS-EFIE formulation produces the same accuracy as the V-EFIE based solution but with a substantially reduced the number of degrees of freedom in its Moment Method discretization. The number of unknowns in the proposed SVS-EFIE is approximately the square-root of the number of degrees of freedom in the standard V-EFIE.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".