An improvement to the spatial discretisation in the Astrophysical Weighted Particle Hydrodynamics method
Abstract
The discretisation of space in the Astrophysical Weighted Particle Hydrodynamics method is attained through a partition-of-unity-based cubature rule. The node (particle) weights in such rules must in general be obtained using approximations, for which only one has been thus far proposed in the literature. In this work, new approximations for these weights are proposed, their properties are studied, and their impact on the accuracy of the cubature rule and the overall method is assessed. Approximations for node centroids are also proposed and studied, and their possible applications are laid out. Additionally, for schemes in which the kernel-function compact-support size is set to be constant, rather than adaptive, weight and centroid approximations are provided as well. Finally, for the cubature rule arising from the weight approximation previously proposed in the literature, an asymptotic expression for its mean relative error is derived, and its usefulness for understanding the finite-sample properties of the cubature rule is showcased with some simple examples.
Versions
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BibTeX
@misc{acha2026improvement,
title = {{An improvement to the spatial discretisation in the Astrophysical Weighted Particle Hydrodynamics method}},
author = {Alex Massaro Achá and Isaac Alonso Asensio and Claudio Dalla Vecchia},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28006},
eprint = {2610.28006},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28006},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An improvement to the spatial discretisation in the Astrophysical Weighted Particle Hydrodynamics method
AU - Alex Massaro Achá
AU - Isaac Alonso Asensio
AU - Claudio Dalla Vecchia
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.28006
UR - https://arxiv.org/abs/2610.28006
AB - The discretisation of space in the Astrophysical Weighted Particle Hydrodynamics method is attained through a partition-of-unity-based cubature rule. The node (particle) weights in such rules must in general be obtained using approximations, for which only one has been thus far proposed in the literature. In this work, new approximations for these weights are proposed, their properties are studied, and their impact on the accuracy of the cubature rule and the overall method is assessed. Approximations for node centroids are also proposed and studied, and their possible applications are laid out. Additionally, for schemes in which the kernel-function compact-support size is set to be constant, rather than adaptive, weight and centroid approximations are provided as well. Finally, for the cubature rule arising from the weight approximation previously proposed in the literature, an asymptotic expression for its mean relative error is derived, and its usefulness for understanding the finite-sample properties of the cubature rule is showcased with some simple examples.
ER -