DISCRETE LAPLACE–BELTRAMI OPERATOR ON SPHERE AND OPTIMAL SPHERICAL TRIANGULATIONS-Reference-Cited by-同舟云学术

DISCRETE LAPLACE–BELTRAMI OPERATOR ON SPHERE AND OPTIMAL SPHERICAL TRIANGULATIONS

Published:2006-02 Issue:01 Volume:16 Page:75-93
ISSN:0218-1959
Container-title:International Journal of Computational Geometry & Applications
language:en
Short-container-title:Int. J. Comput. Geom. Appl.

Author:

XU GUOLIANG¹

Affiliation:

1. LSEC, Institute of Computational Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100080, China

Abstract

In this paper we first modify a widely used discrete Laplace-Beltrami operator proposed by Meyer et al over triangular surfaces, and then we show that the modified discrete operator has some convergence properties over the triangulated spheres. A sequence of spherical triangulations which is optimal in certain sense and leads to smaller truncation error of the discrete Laplace-Beltrami operator is constructed. Optimal hierarchical spherical triangulations are also given. Truncation error bounds of the discrete Laplace-Beltrami operator over the constructed triangulations are provided.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Computational Mathematics,Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218195906001938

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