B-spline patches and transfinite interpolation method for PDE controlled simulation |
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Authors: | Yuanjie Liu Hongbo Li |
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Institution: | School of the Chinese Academy of Sciences,Beijing 100049,China. Hongbo LI Institute of Systems Science,Academy of Mathematics and Systems Science,Chinese Academy of Sciences, Beijing 100190,China. |
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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. |
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