B-SPLINE PATCHES AND TRANSFINITE INTERPOLATION METHOD FOR PDE CONTROLLED SIMULATION

作     者：Yuanjie LIU Hongbo LI 

作者机构：Institute of Systems ScienceAcademy of Mathematics and Systems ScienceChinese Academy of Sciences Graduate School of the Chinese Academy of Sciences 

出 版 物：《Journal of Systems Science & Complexity》 (系统科学与复杂性学报（英文版）)

年 卷 期：2012年第25卷第2期

页      面：348-361页

核心收录：

学科分类：0810[工学-信息与通信工程] 1205[管理学-图书情报与档案管理] 07[理学] 070102[理学-计算数学] 0701[理学-数学] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：partially supported by NKBRSF under Grant No.2011CB302404 NSFC under Grant Nos. 10871195,10925105,60821002,and 50875027 

主　　题：控制模拟 插值方法 超限插值 EB样条 补丁 PDE 偏微分方程 线性系统 

摘      要：This paper is to discuss an approach which combines B-spline patches and transfinite interpolation to establish a linear algebraic system for solving partial differential equations and modify the WEB-spline method developed by Klaus Hollig to derive this new idea.First of all,the authors replace the R-function method with transfinite interpolation to build a function which vanishes on boundaries. Secondly,the authors simulate the partial differential equation by directly applying differential operators to basis functions,which is similar to the RBF method rather than Hollig’s method.These new strategies then make the constructing of bases and the linear system much more straightforward.And as the interpolation is brought in,the design of schemes for solving practical PDEs can be more flexible. This new method is easy to carry out and suitable for simulations in the fields such as graphics to achieve rapid rendering.Especially when the specified precision is not very high,this method performs much faster than WEB-spline method.