Discrete harmonic functions from local coordinates

Tom Bobach, Gerald Farin, Dianne Hansford, Georg Umlauf

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

In this work we focus on approximations of continuous harmonic functions by discrete harmonic functions based on the discrete Laplacian in a triangulation of a point set. We show how the choice of edge weights based on generalized barycentric coordinates influences the approximation quality of discrete harmonic functions. Furthermore, we consider a varying point set to demonstrate that generalized barycentric coordinates based on natural neighbors admit discrete harmonic functions that continuously depend on the point set.

Original languageEnglish (US)
Title of host publicationMathematics of Surfaces XII - 12th IMA International Conference, Proceedings
Pages93-103
Number of pages11
StatePublished - Dec 1 2007
Event12th IMA International Conference on the Mathematics of Surfaces - Sheffield, United Kingdom
Duration: Sep 4 2007Sep 6 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4647 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other12th IMA International Conference on the Mathematics of Surfaces
CountryUnited Kingdom
CitySheffield
Period9/4/079/6/07

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Bobach, T., Farin, G., Hansford, D., & Umlauf, G. (2007). Discrete harmonic functions from local coordinates. In Mathematics of Surfaces XII - 12th IMA International Conference, Proceedings (pp. 93-103). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4647 LNCS).