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A FAST TREECODE FOR MULTIQUADRIC INTERPOLATION WITH VARYING SHAPE PARAMETERS
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DOI：10.1137/110836225.png)
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A treecode algorithm is presented for the fast evaluation of multiquadric radial basis function (RBF) approximations. The method is a dual approach to one presented by Krasny and Wang, which applies far-field expansions to clusters of RBF centers (source points). The new approach clusters evaluation points instead and is therefore easily able to cope with basis functions that have different multiquadric shape parameters. The new treecode is able to evaluate an approximation on N centers at M points in O((N + M) log M) time in the ideal case when evaluation points are uniformly distributed. When coupled with a two-level restricted additive Schwarz preconditioner for GMRES iterations, the treecode is well suited for use within an adaptive RBF iteration, previously described by Driscoll and Heryudono, as is demonstrated by experiments on test functions.
Keyword:
radial basis function interpolation
treecode
restricted additive Schwarz method
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2.6
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PetRBF - A parallel O(N) algorithm for radial basis function interpolation with GaussiansPetRBF-高斯径向基函数插值的并行O(N) 算法
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