Discrete Conservation Laws on Curved Surfaces
Discrete Conservation Laws on Curved Surfaces
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DOI：
10.1137/110846257
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发表时间：
2013-03
期刊：
影响因子：
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通讯作者：
Sheng-Gwo Chen;Jyh-Yang Wu
中科院分区：
文献类型：
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作者：
Sheng-Gwo Chen;Jyh-Yang Wu
本文将介绍一种简单有效的数值方法来计算正则曲面上的标量和向量值函数的微分算子。我们的算法的核心思想是开发一个内在的和统一的方法来直接计算定义在三角网格上的函数的偏导数，三角网格是所考虑的规则曲面的离散化。最重要的是，在三角形网格上完成了扩散方程的发散定理和守恒律。
In this paper we shall introduce a simple, effective numerical method to compute differential operators for scalar and vector-valued functions on regular surfaces. The key idea of our algorithm is to develop an intrinsic and unified way to compute directly partial derivatives of functions defined on triangular meshes which are the discretizations of regular surfaces under consideration. Most importantly, the divergence theorem and conservation laws for diffusion equations on triangular meshes are fulfilled.