Error Analysis and Comparative Study of Numerical Methods for the Parabolic Equation Applied to Tunnel Propagation Modeling
Bibliographic record
Abstract
Parabolic equation (PE) methods have been widely applied to the modeling of wireless propagation in tunnel environments. However, the relevant literature does not include concrete guidelines for the choice of the parameters of these methods and the tradeoffs involved. This paper provides a comprehensive analysis of the two sources of error that arise when PE methods are employed for the modeling of radio-wave propagation scenarios: the well-known numerical dispersion error stemming from the finite-difference solvers for PE and the approximation error stemming from the use of PE for the solution of wave propagation problems that are subject to Maxwell's equations. The analysis is performed for four methods, three of which have been already used in PE-based propagation studies, namely, the Crank-Nicolson (CN) scheme, the alternative-direction-implicit (ADI) method, and its locally one-dimensional (LOD-ADI) version. The fourth method is the Mitchell-Fairweather (MF)-ADI scheme that has been recently shown to be a promising alternative technique for tunnel propagation modeling. The proposed method leads to robust criteria for the choice of spatial discretization in realistic propagation scenarios, as shown via numerical examples.
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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 | 0.005 | 0.019 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".