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

作　　者：Yuanjie LIU Hongbo LI 

机构地区：[1]Institute of Systems Science,Academy of Mathematics and Systems Science,Chinese Academy of Sciences [2]Graduate School of the Chinese Academy of Sciences

出　　处：《Journal of Systems Science & Complexity》2012年第2期348-361,共14页系统科学与复杂性学报（英文版）

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

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 opera- tors 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 flexi- ble. 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 much faster than WEB-spline method. precision is not very high, this method performs

关 键 词：B-spline representation finite element method RBF transfinite interpolation WEB-spline. 

分 类 号：O241.5[理学—计算数学]