@inproceedings{7f08b5f2bf4b4c64a6111a903f49dbde,
title = "Fast sparse kernel summation on Cartesian grids: An on-chip algorithm for 3D implicit surface visualization",
abstract = "This paper proposes a fast algorithm for evaluating sum-mations of heterogenous sparse kernels P of the form s(x) = ΣMi=1 αiφ(ϵi∥x-xi∥) on N points on an arbitrary fine Carte-sian grid in Rd. The algorithm takes the advantage of s-parsity and the structure of Cartesian grids. The sparsity admits operations only be done in some active subsets of the Cartesian grids; the structure of Cartesian grids reduce the storage for N points from O(dN) to O(1), a constant, and thus transforms costly memory intensive operations to cheap computationally intensive operations. This results in scalable algorithm with a complexity of O(N) and makes the postprocessing of large 3D implicit surface feasible on a PC or laptop. Numerical examples for 3D surface reconstruction are presented to illustrate the efficiency of the algorithm.",
keywords = "Kernel summations, Radial basis functions",
author = "Shengxin Zhu and Wathen, {Andrew J.}",
note = "Publisher Copyright: {\textcopyright} 2019 Association for Computing Machinery.; 3rd International Conference on High Performance Compilation, Computing and Communications, HP3C 2019 ; Conference date: 08-03-2019 Through 10-03-2019",
year = "2019",
month = mar,
day = "8",
doi = "10.1145/3318265.3318278",
language = "English",
series = "ACM International Conference Proceeding Series",
publisher = "Association for Computing Machinery",
pages = "20--24",
booktitle = "HP3C 2019 - 2019 the 3rd International Conference on High Performance Compilation, Computing and Communications",
}