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

Imbert-Gérard, Lise-Marie; Greengard, Leslie

doi:10.1002/num.22131

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

Journal Article · Wed Feb 08 23:00:00 EST 2017 · Numerical Methods for Partial Differential Equations

DOI:https://doi.org/10.1002/num.22131· OSTI ID:1532853

Imbert-Gérard, Lise-Marie ^[1]; Greengard, Leslie ^[2]

New York Univ. (NYU), NY (United States). Courant Institute of Mathematical Sciences; DOE/OSTI
New York Univ. (NYU), NY (United States). Courant Institute of Mathematical Sciences; Simons Foundation, New York, NY (United States). Simons Center for Data Analysis

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. In this work, 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.

View Accepted Manuscript (DOE)

Research Organization:: New York Univ. (NYU), NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC); Office of the Assistant Secretary of Defense for Research and Engineering; US Air Force Office of Scientific Research (AFOSR)

Grant/Contract Number:: FG02-88ER25053

OSTI ID:: 1532853

Journal Information:: Numerical Methods for Partial Differential Equations, Journal Name: Numerical Methods for Partial Differential Equations Journal Issue: 3 Vol. 33; ISSN 0749-159X

Publisher:: WileyCopyright Statement

Country of Publication:: United States

Language:: English

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Cited By (3)

Second-kind integral equations for the Laplace-Beltrami problem on surfaces in three dimensions O’Neil, Michael Advances in Computational Mathematics, Vol. 44, Issue 5 https://doi.org/10.1007/s10444-018-9587-7	journal	January 2018
Volumetric variational principles for a class of partial differential equations defined on surfaces and curves: In memory of Heinz-Otto Kreiss Chu, Jay; Tsai, Richard Research in the Mathematical Sciences, Vol. 5, Issue 2 https://doi.org/10.1007/s40687-018-0137-1	journal	April 2018
Second-kind integral equations for the Laplace-Beltrami problem on surfaces in three dimensions O'Neil, Michael arXiv https://doi.org/10.48550/arxiv.1705.00069	preprint	January 2017

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97 MATHEMATICS AND COMPUTING
Genus 1 surfaces
Hodge decomposition
Laplace-Beltrami operator
Mathematics

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

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