Scattered node compact finite difference-type formulas generated from radial basis functions
Journal of Computational Physics
The Runge phenomenon and spatially variable shape parameters in RBF interpolation
Computers & Mathematics with Applications
On choosing a radial basis function and a shape parameter when solving a convective PDE on a sphere
Journal of Computational Physics
A Stable Algorithm for Flat Radial Basis Functions on a Sphere
SIAM Journal on Scientific Computing
Local radial basis function based gridfree scheme for unsteady incompressible viscous flows
Journal of Computational Physics
The use of PDE centres in the local RBF Hermitian method for 3D convective-diffusion problems
Journal of Computational Physics
Stable computation of multiquadric interpolants for all values of the shape parameter
Computers & Mathematics with Applications
Eigenvalue stability of radial basis function discretizations for time-dependent problems
Computers & Mathematics with Applications
Journal of Computational Physics
Stable Computations with Gaussian Radial Basis Functions
SIAM Journal on Scientific Computing
Optimal constant shape parameter for multiquadric based RBF-FD method
Journal of Computational Physics
Computers & Mathematics with Applications
Stable Computations with Gaussian Radial Basis Functions
SIAM Journal on Scientific Computing
Optimal variable shape parameter for multiquadric based RBF-FD method
Journal of Computational Physics
Journal of Computational Physics
Solution to PDEs using radial basis function finite-differences (RBF-FD) on multiple GPUs
Journal of Computational Physics
Stable calculation of Gaussian-based RBF-FD stencils
Computers & Mathematics with Applications
Hi-index | 31.47 |
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. Such node sets provide both geometric flexibility and opportunities for local node refinement. In spite of requiring a somewhat larger total number of nodes for the same accuracy, RBF-generated finite difference (RBF-FD) methods can offer significant savings in computer resources (time and memory). This study presents a new filter mechanism, allowing such gains to be realized also for purely convective PDEs that do not naturally feature any stabilizing dissipation.