2020/08/10 by Patanè, Giuseppe
Computer Science · Engineering · Physics and Astronomy · #Advanced Numerical Analysis Techniques #Computer Graphics and Visualization Techniques #FOS: Computer and information sciences #Graphics (cs.GR) #Model Reduction and Neural Networks
paper · pdf · doi:10.48550/arxiv.2008.04411
openalex publication_date 2020/08/10 · openalex created_date 2022/07/13 · openalex updated_date 2026/07/28
The analysis of vector fields is crucial for the understanding of several\nphysical phenomena, such as natural events (e.g., analysis of waves), diffusive\nprocesses, electric and electromagnetic fields. While previous work has been\nfocused mainly on the analysis of 2D or 3D vector fields on volumes or\nsurfaces, we address the meshless analysis of a vector field defined on an\narbitrary domain, without assumptions on its dimension and discretisation. The\nmeshless approximation of the Helmholtz-Hodge decomposition of a vector field\nis achieved by expressing the potential of its components as a linear\ncombination of radial basis functions and by computing the corresponding\nconservative, irrotational, and harmonic components as solution to a\nleast-squares or to a differential problem. To this end, we identify the\nconditions on the kernel of the radial basis functions that guarantee the\nexistence of their derivatives. Finally, we demonstrate our approach on 2D and\n3D vector fields measured by sensors or generated through simulation.\n