Implicit Function with Natural Behavior over Entire Domain

• ITOH Taku

  Seikei University

• SAITOH Ayumu

  University of Hyogo

• KAMITANI Atsushi

  Yamagata University

• NAKAMURA Hiroaki

  National Institute for Fusion Science

Abstract

To generate a smooth implicit function that behaves naturally over an entire domain, a method to smoothly combine an implicit function f(x) with a global support function g(x) has been proposed. The proposed method can be applied to large scattered point data, since the implicit function f(x) is generated by a partition-of-unity-based method. The global support function g(x) is generated by a radial basis function-based method or by the least-squares method. To ensure a smooth combination of f(x) and g(x), an appropriate weight function is employed. In numerical experiments, the proposed method is applied to large point data. The results illustrate that the proposed method can generate a smooth implicit function F(x) with natural behavior over the entire domain. In addition, on the given points, the accuracy of F(x) is exactly the same as that of f(x). Furthermore, the computational cost for generation of F(x) is almost the same as that of f(x).

Journal

• Plasma and Fusion Research

  Plasma and Fusion Research 7 (0), 2406068-2406068, 2012

  The Japan Society of Plasma Science and Nuclear Fusion Research

Keywords

• implicit function
• meshless method
• extended boundary-node method
• partition of unity
• radial basis function
• smooth combination

Details

• CRID: 1390001205252934784
• NII Article ID: 130004467851
• DOI: 10.1585/pfr.7.2406068
• ISSN: 18806821
• Web Site: https://www.jstage.jst.go.jp/article/pfr/7/0/7_2406068/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed