Near-Optimal Polynomial Interpolation on Spherical Triangles

Sommariva, Alvise; Vianello, Marco

doi:10.1007/s00009-022-01987-7

Cited by 2 publications

(1 citation statement)

References 25 publications

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“…Such thinning processes are also useful in generating multilevel subsets with decreasing separation distances [57] which are useful for multilevel algorithms [53,54,216]. [191] We distinguish this use of oversampled point clouds from another notion also referred to as "oversampling" in which both a fine and a coarse point cloud are used in the simulation, one on the test and another on the trial side of a discretization [96,172].…”

Section: Oversamplingmentioning

confidence: 99%

Point Cloud Generation for Meshfree Methods: An Overview

Suchde

Jacquemin

Davydov

2022

Arch Computat Methods Eng

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Meshfree methods are becoming an increasingly popular alternative to mesh-based methods of numerical simulation. The biggest stated advantage of meshfree methods is the avoidance of generating a mesh on the computational domain. However, even today a surprisingly large amount of meshfree literature ironically uses the nodes of a mesh as the point set that discretizes the domain. On the other hand, already existing efficient meshfree methods to generate point clouds are apparently not very well known among meshfree communities, which has led to recent work redeveloping existing algorithms. In this paper, we present a brief overview of point cloud generation methods for domains and surfaces and discuss their features and challenges, in particular in the context of applicability to industry-relevant complex geometries.

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