VAGO方法求解椭圆型二阶边值问题
VAGO method for the solution of elliptic second-order boundary value problems
AI总结：
本文基于向量分析网格算子（VAGO）方法，利用Delaunay三角剖分和Voronoi图构造差分算子，近似求解一般二阶椭圆方程（包括对流-扩散-反应方程）的边值问题。
摘要：
数学物理问题通常使用向量分析中的微分算子——一阶不变算子，即散度、梯度和旋度算子来表述。在近似求解此类问题时，自然也希望采用类似的算子形式来构造网格问题。VAGO（向量分析网格算子）方法正是基于这一方法论。本文利用Delaunay三角剖分和Voronoi图构造向量分析差分算子，进而采用VAGO方法近似求解一般二阶椭圆方程的边值问题。在对流-扩散-反应方程中，扩散系数为二阶对称张量。
英文摘要：
Mathematical physics problems are often formulated using differential oprators of vector analysis - invariant operators of first order, namely, divergence, gradient and rotor operators. In approximate solution of such problems it is natural to employ similar operator formulations for grid problems, too. The VAGO (Vector Analysis Grid Operators) method is based on such a methodology. In this paper the vector analysis difference operators are constructed using the Delaunay triangulation and the Voronoi diagrams. Further the VAGO method is used to solve approximately boundary value problems for the general elliptic equation of second order. In the convection-diffusion-reaction equation the diffusion coefficient is a symmetric tensor of second order.
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