几何连续曲线上的Laplace-Beltrami方程的等几何分析求解  

Solve Laplace-Beltrami Equation on Geometrically Continuous Curves in Isogeometric Analysis

作　　者：吴梦 王旭辉 倪倩 魏明强[4] Wu Meng;Wang Xuhui;Ni Qian;Wei Mingqiang(School of Mathematics and Statistics,Nanjing University of Science and Technology,Nanjing 210094;College of Science,Hohai University,Nanjing 210098;School of Physical and Mathematical Sciences,Nanjing Tech University,Nanjing 211816;College of Computer Science and Technology,Nanjing University of Aeronautics and Astronautics,Nanjing 211106)

机构地区：[1]南京理工大学数学与统计学院,南京210094 [2]河海大学理学院,南京210098 [3]南京工业大学数理科学学院,南京211816 [4]南京航空航天大学计算机科学与技术学院,南京211106

出　　处：《计算机辅助设计与图形学学报》2021年第12期1916-1922,共7页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(61772167).

摘　　要：复杂计算域上的等几何分析是一个热点问题.通常情况下,复杂计算域可用多片具有几何连续性的简单区域拼接,因此有必要讨论计算域的几何连续性对等几何分析收敛性的影响.针对G1(一阶几何连续)曲线上Laplace-Beltrami方程数值求解问题,从理论上分析了其等几何分析框架下的求解误差,根据理论分析给出了具有最优收敛阶的样条函数空间选择方法.此外,根据样条函数空间的逼近性质,数值上验证了选择的样条函数空间具有最优收敛阶.相关分析初步为复杂计算域的最优收敛的等几何分析提供了理论依据.Research on isogeomatric analysis on a complex computational domain is one of the key problems.Normally a complex computational domain is composed by several simple patches with geometric continuity.Thus,it is necessary to discuss the relationship between the convergence of isogeometric analysis and geometric continuity.Solving Laplace-Beltrami equation on a geometrically continuous curve by analysis isogeometric analysis error theory is discussed.Based on this theoretic result,a method for choosing a spline space to ob-tain an optimal convergence rate in isogeometric solving is introduced and the numerical experiments are il-lustrated.Moreover,we validate the spline space,chosen by its approximate property,reaches the optimal convergence rate numerically.The results provide a theoretical basis for isogeometric analysis on complex computational domains.

关 键 词：等几何分析 几何连续曲线 最优收敛性 样条空间 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]