A new intrinsic numerical method for PDE on surfaces

Abstract

In this note, we introduce a simple, effective numerical method, the local tangential lifting method, for solving partial differential equations for scalar- and vector-valued data defined on surfaces. Even though we follow the traditional way to approximate the regular surfaces under consideration by triangular meshes, 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. We present examples in computer graphics and image processing applications.

Keywords:

• gradient
• Laplacian
• LTL method
• diffusion equations
• surfaces

2010 AMS Subject Classifications :

• 68U05
• 65D25
• 65M99
• 68U07

Acknowledgements

This paper is partially supported by NSC, Taiwan. We would like to thank the editor and referees for their suggestions.