Pseudo-Spectral Methods for the Laplace-Beltrami Equation and the Hodge Decomposition on Surfaces of Genus One

Lise Marie Imbert-Gérard, Leslie Greengard

Research output: Contribution to journalArticle

Abstract

The inversion of the Laplace-Beltrami operator and the computation of the Hodge decomposition of a tangential vector field on smooth surfaces arise as computational tasks in many areas of science, from computer graphics to machine learning to computational physics. Here, we present a high-order accurate pseudo-spectral approach, applicable to closed surfaces of genus one in three-dimensional space, with a view toward applications in plasma physics and fluid dynamics.

Original languageEnglish (US)
Pages (from-to)941-955
Number of pages15
JournalNumerical Methods for Partial Differential Equations
Volume33
Issue number3
DOIs
StatePublished - May 1 2017

Keywords

  • Hodge decomposition
  • Laplace-Beltrami operator
  • genus 1 surfaces

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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