Solution Convergence in Exterior Electromagnetic Boundary Value Problems and Its Dependence on the Numerical Methods-a Review
Bibliographic record
Abstract
In numerical solution of electromagnetic problems, boundary conditions play an essential role to ensure the uniqueness of the solution. The problem may be solved by a variety of methods, such as the integral or differential equation methods, a modal expansion method, or some random application of boundary conditions on the object. In any case, the application of boundary conditions is used to determine the unknown field quantity of the formulation to be used for determining the entire solution in the desired space. The convergence of the solution, therefore, depends on the selection of the unknown and the method used for its determination. However, in exterior boundary value problems the field quantities of interest are at far distances from the boundaries, where the field behaviors are dependent on the entire boundary of the object. Thus, the behaviour of the far field vectors is different from those on the boundary. This problem is investigated here by means of simple scattering by conducting objects having simple, as well as, complex shapes. It is shown that, while the convergence of the solution for determining the boundary fields can be slow, or difficult to obtain, depending on the shape of the object, the convergence of the far field solution is usually more rapid. In particular, the convergence of the far field is mostly dependent on the size of the object, rather than its shape.
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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 | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.002 |
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".