In this paper we give an overview of the Method of Fundamental Solutions (MFS) as a
heuristic numerical method. It is truly meshless. Its concept and numerical implementation …

Radial basis function-generated finite difference (RBF-FD) approximations generalize
classical grid-based finite differences (FD) from lattice-based to scattered node layouts. This …

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 …

In an attempt to introduce application scientists and graduate students to the exciting topic of
positive definite kernels and radial basis functions, this book presents modern theoretical …

Finite differences provided the first numerical approach that permitted large-scale
simulations in many applications areas, such as geophysical fluid dynamics. As accuracy …

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 …

Many radial basis function (RBF) methods contain a free shape parameter that plays an
important role for the accuracy of the method. In most papers the authors end up choosing …

Radial basis function (RBF) approximation is an extremely powerful tool for representing
smooth functions in nontrivial geometries since the method is mesh-free and can be …

Local radial basis function-based differential quadrature method is presented in detail in this
paper. The method is a natural mesh-free approach. Like the conventional differential …

Spectrally accurate interpolation and approximation of derivatives used to be practical only
on highly regular grids in very simple geometries. Since radial basis function (RBF) …