Discrete Conservation Law on Curved Surfaces

2011/09/01 by Chen, Sheng-Gwo, Wu, Jyh-Yang
#Computational Geometry (cs.CG) #Computational Physics (physics.comp-ph) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1109.0129

Abstract

In this paper we shall introduce a simple, effective numerical method for finding differential operators for scalar and vector-valued functions on surfaces. The key idea of our algorithm is to develop an intrinsic and unified way to compute directly the partial derivatives of functions defined on triangular meshes which are the discretization of regular surfaces under consideration. Most importantly, the divergence theorem and conservation laws on triangular meshes are fulfilled.

Related

• A new intrinsic numerical method for PDE on surfaces
• Curvatures of Smooth and Discrete Surfaces
• High-order algorithms for solving eigenproblems over discrete surfaces
• A discrete uniformization theorem for decorated piecewise Euclidean metrics on surfaces
• Discrete Lie Advection of Differential Forms