Harker, Matthew.
2025.
« Least-squares reconstruction of a 3D potential from its measured spatial velocity field ».
In Proceedings of the CSME-CFDSC-CSR 2025 International Congress (Montreal, QC, Canada, May 25-28, 2025)
Coll. « Progress in Canadian Mechanical Engineering », vol. 8.
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Résumé
This paper describes a new method for the least-squares reconstruction of a hypersurface from measured 3D gradient data, for example, the potential function of a measured velocity field. The novel aspect of the proposed algorithm is that the solution relies on representing 3D data with hypermatrices, and obtaining the least-squares solution to the problem as the solution of a hypermatrix equation, i.e., a set of linear equations that equates hypermatrices. The new approach enables the solution of the reconstruction problem over an l x m x n hypersurface in O(n^4) time (with l ~ m ~ n), whereas a straightforward approach of solving the problem with a standard least-squares approach (vectorization) would yield an order O(n^9) algorithm. The new algorithm is therefore five orders of magnitude faster than the state-of-the-art. The new algorithm is tested with synthetic data with synthetic noise. The method is, however, applicable to the problem of reconstructing a potential from velocity data measured, for example, via particle image velocimetry.
| Type de document: | Compte rendu de conférence |
|---|---|
| Éditeurs: | Éditeurs ORCID Hof, Lucas A. NON SPÉCIFIÉ Di Labbio, Giuseppe NON SPÉCIFIÉ Tahan, Antoine NON SPÉCIFIÉ Sanjosé, Marlène NON SPÉCIFIÉ Lalonde, Sébastien NON SPÉCIFIÉ Demarquette, Nicole R. NON SPÉCIFIÉ |
| Professeur: | Professeur Harker, Matthew |
| Affiliation: | Génie des systèmes |
| Date de dépôt: | 18 déc. 2025 15:11 |
| Dernière modification: | 18 déc. 2025 15:11 |
| URI: | https://espace2.etsmtl.ca/id/eprint/32410 |
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