Exact Solution of New Magnetic Current Based Surface-Volume-Surface EFIE and Analysis of Its Spectral Properties
Bibliographic record
Abstract
A novel magnetic current based Surface-Volume-Surface Electric Field Integral Equation (SVS-EFIE-M) is presented for the problem of scattering on homogeneous non-magnetic dielectric objects. The exact Galerkin Method of Moments (MoM) utilizing both the rotational and irrotational vector spherical harmonics as orthogonal basis and test functions according to the Helmholtz decomposition is implemented to solve SVS-EFIE-M analytically for the case of dielectric sphere excited by an electric dipole. The field throughout the sphere is evaluated and compared against the exact classical Mie series solution. The two are shown to agree to 12 digits of accuracy upon a sufficient number of basis/test functions taken in the MoM solution and the Mie series expansion. This exact solution validates the rigorous nature of the new SVS-EFIE-M formulation. It also reveals the spectral properties of its individual operators, their products and their linear combination. The spectrum of the MoM impedance matrix is also obtained. It is shown that upon choosing basis and test functions in$L^{2}(S)$space and evaluating testing inner products in the same space, the MoM impedance matrix features bounded condition number with increasing order of discretization and/or at low frequencies. This makes the proposed SVS-EFIE-M formulation free of oversampling and low-frequency breakdowns giving it advantage both over its SVS-EFIE-J predecessor and classical double-source integral equations such as PMCHWT, Muller, and others suffering from this type of numerical instabilities inherent to their inferior spectral properties.
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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) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".