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

Fingerprint

Beltrami Equation
Hodge Decomposition
Pseudospectral Method
Laplace equation
Laplace's equation
Genus
Physics
Decomposition
Plasma Physics
Laplace-Beltrami Operator
Smooth surface
Computer graphics
Fluid Dynamics
Fluid dynamics
Learning systems
Mathematical operators
Vector Field
Inversion
Machine Learning
Higher Order

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

Cite this

Pseudo-Spectral Methods for the Laplace-Beltrami Equation and the Hodge Decomposition on Surfaces of Genus One. / Imbert-Gérard, Lise Marie; Greengard, Leslie.

In: Numerical Methods for Partial Differential Equations, Vol. 33, No. 3, 01.05.2017, p. 941-955.

Research output: Contribution to journalArticle

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