On the role of polynomials in RBF-FD approximations: I. Interpolation and accuracy
Radial basis function-generated finite difference (RBF-FD) approximations generalize
classical grid-based finite differences (FD) from lattice-based to scattered node layouts. This …
classical grid-based finite differences (FD) from lattice-based to scattered node layouts. This …
[图书][B] A primer on radial basis functions with applications to the geosciences
B Fornberg, N Flyer - 2015 - SIAM
This book is focused on a powerful numerical methodology for solving PDEs to high
accuracy in any number of dimensions: Radial Basis Functions (RBFs). During the past …
accuracy in any number of dimensions: Radial Basis Functions (RBFs). During the past …
[PDF][PDF] The meshless local Petrov-Galerkin (MLPG) method: a simple & less-costly alternative to the finite element and boundary element methods
S Shen - Computer Modeling in Engineering & Sciences, 2002 - cdn.techscience.cn
A comparison study of the efficiency and accuracy of a variety of meshless trial and test
functions is presented in this paper, based on the general concept of the meshless local …
functions is presented in this paper, based on the general concept of the meshless local …
[HTML][HTML] Stable calculation of Gaussian-based RBF-FD stencils
B Fornberg, E Lehto, C Powell - Computers & Mathematics with …, 2013 - Elsevier
Traditional finite difference (FD) methods are designed to be exact for low degree
polynomials. They can be highly effective on Cartesian-type grids, but may fail for …
polynomials. They can be highly effective on Cartesian-type grids, but may fail for …
Stabilization of RBF-generated finite difference methods for convective PDEs
B Fornberg, E Lehto - Journal of Computational Physics, 2011 - Elsevier
Radial basis functions (RBFs) are receiving much attention as a tool for solving PDEs
because of their ability to achieve spectral accuracy also with unstructured node layouts …
because of their ability to achieve spectral accuracy also with unstructured node layouts …
Enhancing finite differences with radial basis functions: experiments on the Navier–Stokes equations
Polynomials are used together with polyharmonic spline (PHS) radial basis functions (RBFs)
to create local RBF-finite-difference (RBF-FD) weights on different node layouts for spatial …
to create local RBF-finite-difference (RBF-FD) weights on different node layouts for spatial …
A guide to RBF-generated finite differences for nonlinear transport: shallow water simulations on a sphere
The current paper establishes the computational efficiency and accuracy of the RBF-FD
method for large-scale geoscience modeling with comparisons to state-of-the-art methods …
method for large-scale geoscience modeling with comparisons to state-of-the-art methods …
A radial basis function (RBF)-finite difference (FD) method for diffusion and reaction–diffusion equations on surfaces
In this paper, we present a method based on radial basis function (RBF)-generated finite
differences (FD) for numerically solving diffusion and reaction–diffusion equations (PDEs) …
differences (FD) for numerically solving diffusion and reaction–diffusion equations (PDEs) …
Optimal constant shape parameter for multiquadric based RBF-FD method
Radial basis functions (RBFs) have become a popular method for interpolation and solution
of partial differential equations (PDEs). Many types of RBFs used in these problems contain …
of partial differential equations (PDEs). Many types of RBFs used in these problems contain …
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 …