A new intrinsic numerical method for PDE on surfaces

TL;DR

This paper introduces an intrinsic numerical method for solving PDEs on surfaces that directly computes derivatives on triangular meshes, applicable in computer graphics and image processing.

Contribution

It presents a novel intrinsic and unified approach to compute derivatives directly on triangular meshes for PDEs on surfaces.

Findings

Effective for scalar and vector PDEs on surfaces

Applicable to computer graphics and image processing

Simplifies derivative computation on meshes

Abstract

In this note we shall introduce a simple, effective numerical method for solving partial differential equations for scalar and vector-valued data defined on surfaces. Even though we shall 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 shall present examples in computer graphics and image processing applications.