Wavelet-based multiresolution algorithm for integral and boundary element equations in electric and magnetic field computations
Bibliographic record
Abstract
Summary form only given. The wavelet algorithm for integral equations was first studied by Beylkin et al.(1991). When applied to electric and magnetic field problems formulated in terms of the method of moments (MoM) or the boundary element method (BEM), it was recognized that the wavelet transform (WT) yielded a sparse algebraic equation matrix. However, when the domain was discretized with regular basis functions, for example piecewise constant or piecewise linear, it was necessary to allocate extra memory for the transformed matrix. Moreover, the transformed matrix did not appear to have a better condition number than that of the original one. We use wavelet functions as both basis and weight functions to obtain a reasonable trade-off between the entire domain and subsectional basis functions. The whole domain may be divided into several subsections. In each subsection, the higher resolution basis is incorporated, thus preserving the merits of entire domain basis functions while yielding a sparse matrix. The wavelet-based multiresolution algorithm is described in the full paper and numerical examples are presented to illustrate its flexibility.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".