【摘 要】
：
In recent years,a fast radial basis function(RBF)solver for surface interpolation has been developed by Karageorghis et al.[1].In this presentation,we follo
【机 构】
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College of Mathematics,Taiyuan University of Technology,China
【出 处】
：
第7届Trefftz工程计算方法(ICTM2015)暨第3届基本解工程应用方法(MFS)
论文部分内容阅读
In recent years,a fast radial basis function(RBF)solver for surface interpolation has been developed by Karageorghis et al.[1].In this presentation,we follow up their work by extending the idea of fast evaluation of the surface interpolation to efficiently solve various types of partial differential equations(PDEs).We look into the possibility of solving PDEs with conformal mapping to map the RBF circular points on a disk to the interior of an irregular domain.We also compare the pros and cons for these two approaches.In both approaches,the circulant matrix formulation and the matrix decomposition method are the central ideas of fast computation.The method of particular solutions is introduced to turn the function interpolation problems into solving problems containing PDEs.After the particular solution is obtained,the method of fundamental solutions [2,3] is applied to find the homogeneous solutions.Several numerical examples are given to show the greater accuracy and efficiency of the proposed approaches.In numerical experiments,we test these two approaches for solving PDEs using up to 160,000 RBF interpolation points with greater accuracy and efficiency.
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