Wavelet-based solution of integral equations for acoustic scattering
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 o f shifted and dilated forms o f a properly chosen mother wavelet.The wavelet expansion covers the scatterer surface for distributing the wavelet localized functions.A simpler formulation o f a square wavelet operator is proposed and tested in this investigation to obtain the moment matrix.The proposed operator saves some traditional stages o f 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 o f the computational load.The accuracy o f the proposed solution is compared to the exact solution o f the problem.Computational savings are illustrated for acoustic scattering on a sphere for different wave numbers and wavelet bases order. s o m m a ir eDans ce travail, l 'analyse de ondelette est employee pour résoudre l 'équation intégrale de Helmholtz pour la dispersion acoustique.L'équation intégrale est résolue en utilisant la méthode de moment avec la base de ondelette.Le champ inconnu est exprimé comme une addition de deux fois des formes décalées et dilatées d'un ondelette correctement choisi de mère.L'expansion de ondelette couvre la surface de diffuseur pour distribuer les functions localisées par ondelette.Un opérateur carré de ondelette est propose dans une formulation plus simple et examiné pour que ce problème obtienne la matrice de moment.L'opérateur proposé sauve quelques étapes traditionnelles de ondelette transforment et en conséquence une partie des calculs priés.L'inversion carrée de matrice peut être mise en application facilement sur différents médias.L'application d 'un seuil approprié sur la matrice résultante la rend clairsemée.La solution d 'une telle matrice clairsemée sauve une grande partie du volume des calculs.L'exactitude de la solution proposée est examinée par l 'intermédiaire de la comparaison avec la solution exacte du problème.L'épargne informatique est illustrée pour la dispersion acoustique sur une sphère pour des nombres de vague et l'ordre différents de bases de ondelette.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| 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 | 0.001 |
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".