基于角点处扭矢构造双三次Coons曲面的一种优化方法  

An optimal method for constructing bicubically Coons surfaces based on twists at corner points

作　　者：韩旭里[1] 韩靖[1] 朱远鹏[1] 

机构地区：[1]中南大学数学与统计学院,长沙410083

出　　处：《中国科学：数学》2014年第7期805-814,共10页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:60970097和11271376);湖南省研究生科研创新(批准号:CX2012B111)资助项目

摘　　要：本文针对矩形网格角点处的扭矢采用优化方法构造双三次Coons曲面,提出一种新的优化准则来确定角点处的扭矢.首先,通过变分原理,考虑曲面导矢的极小化问题转化的Euler-Lagrange偏微分方程,将该方程应用于每一个Coons块的角点上,引入一个新的极小化问题,其解是Euler-Lagrange偏微分方程的近似最优解.然后,建立一个具有块三对角系数矩阵的线性方程组来求解新的极小化问题.该系数矩阵可以表示为两个相同的形式特殊的矩阵的Kronnecker积,进而可以证明其非奇异性.最后,数值实验验证本文方法的稳定性和有效性.This paper presents an optimal method for constructing bicubically Coons surface based upon twist vectors at rectangular grid points. These twists are determined by using a new optimal criterion. By variational principle, the minimization problem is based on the Euler-Lagrange PDE. By applying it at corner points on each patch, we introduce a new minimization problem, whoes solution is approximately optimal for Euler-Lagrange PDE on every patch. A linear equations system with symmetrical block tridiagonal coefficient matrix is established to solve the minimization problem. Its coefficient matrix, which can be written as the Kronecker product of two identical interesting special matrices, is proved to be non-singular. Numerical solution is stable and examples validate its effectiveness.

关 键 词：COONS曲面 扭矢 优化 对称块三对角矩阵 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]