Novel single-source surface integral equations for scattering on 2-D penetrable cylinders and current flow modeling in 2-D and 3-D conductors
Bibliographic record
Abstract
Accurate modeling of current flow and network parameter extraction in 2-D and 3-D conductors has an important application in signal integrity of high-speed interconnects. In this thesis, we propose a new rigorous single-source Surface-Volume-Surface Electric Field Integral Equation (SVS-EFIE) for magnetostatic analysis of 2-D transmission lines and broadband resistance and inductance extraction in 3-D interconnects. Furthermore, the novel integral equation can be used for the solution of full-wave scattering problems on penetrable 2-D cylinders of arbitrary cross-section under transverse magnetic polarization. The new integral equation is derived from the classical Volume Electric Field Integral Equation (V-EFIE) by representing the electric field inside a conductor or a scatterer as a superposition of the cylindrical waves emanating from the conductor’s surface. This converts the V-EFIE into a surface integral equation involving only a single unknown function on the surface. The novel equation features a product of integral operators mapping the field from the conductor surface to its volume and back to its surface terming the new equation the Surface-Volume-Surface EFIE. The number of unknowns in the proposed SVS-EFIE is approximately the square root of the number of degrees of freedom in the traditional V-EFIE; therefore, it allows for substantially faster network parameter extraction and solutions to 2-D scattering problems without compromising the accuracy. The validation and benchmark of the numerical implementation of the Method of Moment discretization of the novel SVS-EFIE has been done via comparisons against numerical results obtained by using alternative integral equations, data found in literature, simulation results acquired from the CAD software, and analytic formulas.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 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 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".