A Closed-Form Formula for the RBF-Based Approximation of the Laplace–Beltrami Operator

• Published in: Journal of scientific computing Vol. 77; no. 2; pp. 1115 - 1132
• Main Authors: Álvarez, Diego, González-Rodríguez, Pedro, Moscoso, Miguel
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.11.2018; Springer Nature B.V
• Subjects: Algorithms; Approximation; Cardiology; Closed form solutions; Computational Mathematics and Numerical Analysis; Curvature; Exact solutions; Mathematical analysis; Mathematical and Computational Engineering; Mathematical and Computational Physics; Mathematics; Mathematics and Statistics; Methods; Nodes; Operators (mathematics); Partial differential equations; Radial basis function; Theoretical; Radial basis functions; 65D05; 35R01; 58J05; Cardiology; Surface PDE; Surface Laplacian

In this paper we present a method that uses radial basis functions to approximate the Laplace–Beltrami operator that allows to solve numerically diffusion (and reaction–diffusion) equations on smooth, closed surfaces embedded in R 3 . The novelty of the method is in a closed-form formula for the Lap...