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Journal of Systems Science and Complexity

, Volume 25, Issue 2, pp 348–361 | Cite as

B-spline patches and transfinite interpolation method for PDE controlled simulation

  • Yuanjie LiuEmail author
  • Hongbo Li
Article

Abstract

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.

Key words

B-spline representation finite element method RBF transfinite interpolation WEB-spline 

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Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, CAS and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Institute of Systems Science, Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina
  2. 2.Graduate School of the Chinese Academy of SciencesBeijingChina

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