Wavelet-based solution of integral equations for acoustic scattering
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Bibliographic record
Abstract
In this work, the multi-resolution wavelet analysis is used to solve Helmholtz integral equation for acoustic scattering. The integral equation is solved using moment method with wavelet basis. The unknown field is expressed as a two fold summation of shifted and dilated forms of a properly chosen mother wavelet. The wavelet expansion covers the scatterer surface for distributing the wavelet localized functions. A simpler formulation of a square wavelet operator is proposed and tested in this investigation to obtain the moment matrix. The proposed operator saves some traditional stages of wavelet transform and accordingly a part of the computations required. The square matrix inversion can be implemented easily on different media. The resulting matrix can be made sparse by applying an appropriate threshold. The solution of such sparse matrix saves a large portion of the computational load. The accuracy of the proposed solution is compared to the exact solution of the problem. Computational savings are illustrated for acoustic scattering on a sphere for different wave numbers and wavelet bases order.
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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 it