Discrete Harmonic Functions from Local Coordinates

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.

• Type: Conference
• Year: 2007
• Where: IMAMS
• Authors: Tom Bobach, Gerald E. Farin, Dianne Hansford, Georg Umlauf
• Keywords: Continuous Harmonic Functions, Discrete Harmonic Functions, Discrete Laplacian, IMAMS 2007, Mathematics