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

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 t...

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Bibliographic Details
Published in:Journal of systems science and complexity 2012-04, Vol.25 (2), p.348-361
Main Authors: Liu, Yuanjie, Li, Hongbo
Format: Article
Language:English
Subjects:
Complex Systems
Control
EB样条
Mathematics
Mathematics and Statistics
Mathematics of Computing
Operations Research/Decision Theory
PDE
Statistics
Systems Theory
偏微分方程
控制模拟
插值方法
线性系统
补丁
超限插值
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Summary: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
ISSN:1009-6124
1559-7067
DOI:10.1007/s11424-012-1148-4