Kernel techniques: from machine learning to meshless methods
R Schaback, H Wendland - Acta numerica, 2006 - cambridge.org
Kernels are valuable tools in various fields of numerical analysis, including approximation,
interpolation, meshless methods for solving partial differential equations, neural networks …
interpolation, meshless methods for solving partial differential equations, neural networks …
[图书][B] Computational partial differential equations using MATLAB®
In this popular text for an Numerical Analysis course, the authors introduce several major
methods of solving various partial differential equations (PDEs) including elliptic, parabolic …
methods of solving various partial differential equations (PDEs) including elliptic, parabolic …
Stable computations with flat radial basis functions using vector-valued rational approximations
GB Wright, B Fornberg - Journal of Computational Physics, 2017 - Elsevier
One commonly finds in applications of smooth radial basis functions (RBFs) that scaling the
kernels so they are 'flat'leads to smaller discretization errors. However, the direct numerical …
kernels so they are 'flat'leads to smaller discretization errors. However, the direct numerical …
Preconditioning for radial basis functions with domain decomposition methods
L Ling, EJ Kansa - Mathematical and Computer modelling, 2004 - Elsevier
In our previous work, an effective preconditioning scheme that is based upon constructing
least-squares approximation cardinal basis functions (ACBFs) from linear combinations of …
least-squares approximation cardinal basis functions (ACBFs) from linear combinations of …
Domain decomposition for radial basis meshless methods
Both overlapping and nonoverlapping domain decomposition methods (DDM) on matching
and nonmatching grid have been developed to couple with the meshless radial basis …
and nonmatching grid have been developed to couple with the meshless radial basis …
A least-squares preconditioner for radial basis functions collocation methods
L Ling, EJ Kansa - Advances in Computational Mathematics, 2005 - Springer
Although meshless radial basis function (RBF) methods applied to partial differential
equations (PDEs) are not only simple to implement and enjoy exponential convergence …
equations (PDEs) are not only simple to implement and enjoy exponential convergence …
A Not-a-Knot meshless method using radial basis functions and predictor–corrector scheme to the numerical solution of improved Boussinesq equation
A numerical simulation of the improved Boussinesq (IBq) equation is obtained using
collocation and approximating the solution by radial basis functions (RBFs) based on the …
collocation and approximating the solution by radial basis functions (RBFs) based on the …
Radial basis function method for 1-D and 2-D groundwater contaminant transport modeling
In this paper we develop a meshless method for modeling groundwater contaminant
transport. The algorithm uses collocation method with radial basis functions. Numerical …
transport. The algorithm uses collocation method with radial basis functions. Numerical …
[PDF][PDF] A practical guide to radial basis functions
R Schaback - Electronic Resource, 2007 - researchgate.net
This is “my” part of a future book “Scientific Computing with Radial Basis Functions” I am
currently writig with my colleagues CS Chen and YC Hon. I took a preliminary version out of …
currently writig with my colleagues CS Chen and YC Hon. I took a preliminary version out of …
Radial basis functions methods for solving Fokker–Planck equation
In this paper two numerical meshless methods for solving the Fokker–Planck equation are
considered. Two methods based on radial basis functions to approximate the solution of …
considered. Two methods based on radial basis functions to approximate the solution of …