A fast algorithm for particle simulations
Journal of Computational Physics
Knot removal for parametric B-spline curves and surfaces
Computer Aided Geometric Design
Fast Evaluation of Radial Basis Functions: Moment-Based Methods
SIAM Journal on Scientific Computing
A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems
SIAM Journal on Scientific Computing
Fast Solution of the Radial Basis Function Interpolation Equations: Domain Decomposition Methods
SIAM Journal on Scientific Computing
Polynomials and Potential Theory for Gaussian Radial Basis Function Interpolation
SIAM Journal on Numerical Analysis
Computers & Mathematics with Applications
Fast Radial Basis Function Interpolation via Preconditioned Krylov Iteration
SIAM Journal on Scientific Computing
Meshfree Approximation Methods with MATLAB
Meshfree Approximation Methods with MATLAB
A Cartesian treecode for screened coulomb interactions
Journal of Computational Physics
Fast Evaluation of Multiquadric RBF Sums by a Cartesian Treecode
SIAM Journal on Scientific Computing
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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.