On choosing a radial basis function and a shape parameter when solving a convective PDE on a sphere
Journal of Computational Physics
Multi-level meshless methods based on direct multi-elliptic interpolation
Journal of Computational and Applied Mathematics
Fast radial basis function interpolation with Gaussians by localization and iteration
Journal of Computational Physics
An SVD analysis of equispaced polynomial interpolation
Applied Numerical Mathematics
Rational radial basis function interpolation with applications to antenna design
Journal of Computational and Applied Mathematics
Global field interpolation for particle methods
Journal of Computational Physics
The uselessness of the Fast Gauss Transform for summing Gaussian radial basis function series
Journal of Computational Physics
Application of the RBF meshless method to the solution of the radiative transport equation
Journal of Computational Physics
Heart surface motion estimation framework for robotic surgery employing meshless methods
IROS'09 Proceedings of the 2009 IEEE/RSJ international conference on Intelligent robots and systems
Discretization correction of general integral PSE Operators for particle methods
Journal of Computational Physics
Fast and accurate interpolation of large scattered data sets on the sphere
Journal of Computational and Applied Mathematics
Applied Numerical Mathematics
A high order multivariate approximation scheme for scattered data sets
Journal of Computational Physics
RBF-FD formulas and convergence properties
Journal of Computational Physics
Design of fractional order digital differentiator using radial basis function
IEEE Transactions on Circuits and Systems Part I: Regular Papers
Adaptive meshless centres and RBF stencils for Poisson equation
Journal of Computational Physics
Scattered data interpolation and approximation for computer graphics
ACM SIGGRAPH ASIA 2010 Courses
An alternative procedure for selecting a good value for the parameter c in RBF-interpolation
Advances in Computational Mathematics
Applied Numerical Mathematics
Efficient MFS Algorithms for Inhomogeneous Polyharmonic Problems
Journal of Scientific Computing
Compact local integrated-RBF approximations for second-order elliptic differential problems
Journal of Computational Physics
Spectral collocation and radial basis function methods for one-dimensional interface problems
Applied Numerical Mathematics
Optimal constant shape parameter for multiquadric based RBF-FD method
Journal of Computational Physics
Computers & Mathematics with Applications
Error-controlled global sensitivity analysis of ordinary differential equations
Journal of Computational Physics
Fast Evaluation of Multiquadric RBF Sums by a Cartesian Treecode
SIAM Journal on Scientific Computing
A rational Arnoldi approach for ill-conditioned linear systems
Journal of Computational and Applied Mathematics
CAD and mesh repair with Radial Basis Functions
Journal of Computational Physics
MICAI'11 Proceedings of the 10th international conference on Artificial Intelligence: advances in Soft Computing - Volume Part II
Journal of Computational Physics
Quasi-interpolation for linear functional data
Journal of Computational and Applied Mathematics
Multivariate interpolation with increasingly flat radial basis functions of finite smoothness
Advances in Computational Mathematics
A fast object-oriented Matlab implementation of the Reproducing Kernel Particle Method
Computational Mechanics
Computers & Mathematics with Applications
A Fast Treecode for Multiquadric Interpolation with Varying Shape Parameters
SIAM Journal on Scientific Computing
Stable Evaluation of Gaussian Radial Basis Function Interpolants
SIAM Journal on Scientific Computing
On Dimension-independent Rates of Convergence for Function Approximation with Gaussian Kernels
SIAM Journal on Numerical Analysis
Preconditioning linear systems via matrix function evaluation
Applied Numerical Mathematics
International Journal of Numerical Modelling: Electronic Networks, Devices and Fields
Full length article: A scheme for interpolation by Hankel translates of a basis function
Journal of Approximation Theory
Multivariate polynomial interpolation and meshfree differentiation via undetermined coefficients
Journal of Computational and Applied Mathematics
A study of different modeling choices for simulating platelets within the immersed boundary method
Applied Numerical Mathematics
Swarm interpolation using an approximate chebyshev distribution
ANTS'12 Proceedings of the 8th international conference on Swarm Intelligence
Journal of Computational Physics
Applied Numerical Mathematics
A compact five-point stencil based on integrated RBFs for 2D second-order differential problems
Journal of Computational Physics
Advances in Computational Mathematics
A stochastic minimum principle and an adaptive pathwise algorithm for stochastic optimal control
Automatica (Journal of IFAC)
Generalized Hermitian Radial Basis Functions Implicits from polygonal mesh constraints
The Visual Computer: International Journal of Computer Graphics
The role of inner summaries in the fast evaluation of thin-plate splines
Advances in Computational Mathematics
Journal of Computational Physics
Least-squares hermite radial basis functions implicits with adaptive sampling
Proceedings of Graphics Interface 2013
Algebraic cubature by linear blending of elliptical arcs
Applied Numerical Mathematics
A meshless method for the numerical computation of the solution of steady Burgers-type equations
Applied Numerical Mathematics
A radial basis function method for solving PDE-constrained optimization problems
Numerical Algorithms
Journal of Approximation Theory
Wendland functions with increasing smoothness converge to a Gaussian
Advances in Computational Mathematics
Original article: Recovering functions: A method based on domain decomposition
Mathematics and Computers in Simulation
A meshless interpolation algorithm using a cell-based searching procedure
Computers & Mathematics with Applications
Hi-index | 0.09 |
Meshfree approximation methods are a relatively new area of research, and there are only a few books covering it at present. Whereas other works focus almost entirely on theoretical aspects or applications in the engineering field, this book provides the salient theoretical results needed for a basic understanding of meshfree approximation methods. The emphasis here is on a hands-on approach that includes MATLAB routines for all basic operations. Meshfree approximation methods, such as radial basis function and moving least squares method, are discussed from a scattered data approximation and partial differential equations point of view. A good balance is supplied between the necessary theory and implementation in terms of many MATLAB programs, with examples and applications to illustrate key points. Used as class notes for graduate courses at Northwestern University, Illinois Institute of Technology, and Vanderbilt University, this book will appeal to both mathematics and engineering graduate students.